Friday, August 12, 2016

Correlations and Entanglement swapping

take 2

Finally I am ready to discuss the topic I promised: entanglement swapping. This s not a hard topic, and in fact it is usually given as a homework problem but since Lubos insists on doubling and tripling down on the fact that quantum correlations can arise only due to prior interaction:

"Whenever there's some correlation in the world – in our quantum world – it's a consequence of the two subsystems' interactions (or common origin) in the past."

"Of course I stand by the statement. Causality/locality implies that any entanglement - or any correlation - between objects in two places has to result from their contact or interaction in the intersection of their past light cones."

I want to work out the problem in detail for anyone interested to see under what conditions two particles can become entangled even though they never interacted.

Let me start with the usual Bell states:

\(|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle)+|11\rangle)\)
\(|\Phi^-\rangle = \frac{1}{\sqrt{2}}(|00\rangle)-|11\rangle)\)
\(|\Psi^+\rangle = \frac{1}{\sqrt{2}}(|01\rangle)+|10\rangle)\)
\(|\Psi^-\rangle = \frac{1}{\sqrt{2}}(|01\rangle)-|10\rangle)\)

and have two pairs of Bell particles (which do originate as Lubos demands from a common origin in the past). It does not matter which Bell states we start with and for the sake of the example let's pick the following 4 particles in the state below:

\(|1234\rangle = |\Psi^-\rangle_{12}|\Psi^-\rangle_{34}= \frac{1}{2}(|0101\rangle-|0110\rangle-|1001\rangle+|1010\rangle)\)

Now suppose that the first pair  \(|\Psi^-\rangle_{12}\) is split between Alice and Charlie, and the second pair \(|\Psi^-\rangle_{34}\) is split between Charlie and Bob such that Alice has particle 1, Charlie has particles 2 and 3, and Bob has particle 4. Particles 1 and 2 share a common origin, and the same is true for particles 3 and 4, but particles 1 and 4 NEVER interacted in the past.

Now Charlie does a projective  measurement on say \(\Phi^+\) on particles 2 and 3:

\(P_{\Phi^+} = \frac{1}{2}(|00\rangle+|11\rangle)(\langle00|+\langle11|)\)
\(P_{\Phi^+} = \frac{1}{2}(|00\rangle\langle00| + |00\rangle\langle11| + |11\rangle\langle00| + |11\rangle\langle11|)\)

This means that we apply the projector:

\(I_1 \otimes P_{\Phi^{+}_{23}}\otimes I_4\) on \(|1234\rangle \):

Ignoring the overall normalization factors for simplicity sake this means we need to compute:

\(|00\rangle_{23}\langle00| + |00\rangle_{23}\langle11| + |11\rangle_{23}\langle00| + |11\rangle_{23}\langle11|)\)

\(-|1001\rangle - |0000\rangle - |1111\rangle - |0110\rangle= \)

\(-(|11\rangle+|00\rangle)_{14}|00\rangle_{23} -  (|11\rangle+|00\rangle)_{14}|11\rangle_{23} = \)

\(-(|11\rangle+|00\rangle)_{14} (|11\rangle+|00\rangle)_{23} = - |\Phi^+\rangle_{14}|\Phi^+\rangle_{23}\)

and now particles 1 and 4 are entangled despite never interacting in the past.

So how does Lubos explain this?

"In quantum information, this is a part of the "LOCC" ("local operations and classical computation" do not create or increase entanglement) principle"

True but irrelevant. LOCC cannot increase entanglement overall, but now two particles which never interacted became entangled.

"Entanglement swapping is surely not a counterexample of LOCC, there can't be any counterexample. It's just swapping."

Again true but irrelevant.

"It's like the entanglement is riding on a train A and changes the trains to another train B that happens to meet A at some point."

This is fuzzy handwaving talk. It is true one can do correlation swapping in the classical world: suppose Alice has left and right gloves and she puts them in a bag. Bob does the same thing with his gloves and Charlie picks up a glove from Alice's bag and one from Bob's bag. Upon inspection of what he extracted he know how the gloves left in the two bags are correlated. However in the quantum case things are qualitatively different because of the active role of the observer and the fact that the result of measurement does not exist before measurement. I think I know where Lubos is coming from. I am speculating that he truly believes that quantum correlations are like Beltramann' socks, and if so his position makes perfect sense. However this is an unsustainable position and I plan to show why in subsequent posts. Lubos war on Bell is unsustainable as well. If you want to criticize Bell you have to do it on his genuine fault: the idea of beables. But this is a topic for another day, Let's continue:

"So the pair entangled afterwards is described differently after the trains are switched but the entanglement is preserved and links two places that change continuously and at most by the speed of light."

This is a crackpot statement. The introduction of the speed of light arguments illustrates a fundamental misunderstanding. Basically here Lubos attempts to come up with a handwaving argument of sliding the light cones of particles 1 and 4 until overlap for the purpose of generating correlation. Collapse in the classical and the quantum world is the result of information being revealed. There is no such thing as a propagation of collapse and/or correlation at the speed of light or slower. Any talk of propagation of collapse/correlation is nonsense.

I am pretty sure Lubos will counter this and  attempt to clean the handwaving but if he is precise he will have to pick between two unacceptable options: (1) introducing considerations of propagation of correlations or (2) explain the 1 and 4 particle entanglement similar with my gloves example above and contradicting the role of the observer. If I were to make a prediction he is going to pick option 2 and argue that quantum correlations are precisely like Beltramann' socks.   

"Why teleportation isn't a counterexample - or a source of nonlocality - was also discussed in detail in Susskind's recent arXiv:1604.02589."

Here I talk about entanglement swapping, not teleportation. True they are closely related, and true, entanglement is not created by LOCC. Again the contention is on this statement: "Causality/locality implies that any entanglement - or any correlation - between objects in two places has to result from their contact or interaction in the intersection of their past light cones"
which is proven false by the computation above.

It is always dangerous to make grandiose statements using "all", "any", etc.

I won't get into the ER=EPR argument, but at some point in the future I'll explain why it is irrelevant in the quantum foundation/interpretation area.

"Feel free to write another completely wrong blog post - you have already written dozens of those - this URL is one giant pseudointellectual dumping ground."

On quantum interpretation, both me and Lubos are in the Copenhagen camp and I (civilly and without burning bridges) disagree more with the Bohmian or the MWI positions than with Lubos. From 10,000 feet if you do not care about subtle points and excluding his vitriol Lubos is basically correct in his quantum mechanics intuition.

However there is a fundamental difference between us: I am (neo) Copenhagen because my work proved to me this is the correct point of view while Lubos is a self-appointed defender of quantum orthodoxy. Lubos shoots from the hip, is not aware of subtle points in quantum mechanics, and hides his ignorance by ad hominem attacks. I do not care about him being a jerk any more than I care about being criticized for not wearing pink slippers at work. I do care very much however about being right and if I am proven wrong I do acknowledge my mistakes (nobody is perfect). Like Trump, Lubos never acknowledges mistakes and doubles and triples down. And I just could not resist calling the emperor naked when this happens.  


  1. You're just being silly. The correlation between 1 and 4 is a correlation between the subsystems separated as 1+2 and 3+4, and these systems have clearly interacted with each other: the joint-property measurement of 2,3 is this interaction. So this joint-property measurement is what explains the correlation between 1 and 4, too.

  2. I wrote a longish blog post but at the end, I included a concise explanation what's going on. My A1,A2,B1,B2 are your 1,2,3,4. The (qu)bits have values 0,1 and XOR is addition modulo two.

    The correct solution is:

    There is no correlation between A1 and B2 independently of other measurements. The correlation only exists given a particular result of the joint measurement of A2 XOR B1. For this reason, the actual observed correlation that exists is not among two measured quantities A1 and B2 but among three measured quantities A1, A2 XOR B1, and B2. The correlation is such that

    A1 XOR (A2 XOR B1) XOR B2 = 0

    This actual correlation between three variables E=A1, F=A2 XOR B1, G=B2 doesn't violate locality because the measurements E and F (and similarly F and G) have common causes in the shared past light cones (the production of the pairs at sources). That's enough to explain the correlation (the non-factorization of the probability distribution for E,F,G). There doesn't have to be a shared event in the past between any pair of the variables in the list E,F,G.

    In particular, there's no need for the past light cones of the measurements E,G to overlap (have common causes): the overlap of the past light cones of E,F and similarly F,G is enough to explain the correlation between E,F,G!

    Indeed, the correlation between E,F,G above is easy to verify by commutativity and associatity of XOR:

    A1 XOR (A2 XOR B1) XOR B2 =
    = (A1 XOR A2) XOR (B1 XOR B2) =
    = 1 XOR 1 = 0.

    This works for colors of socks just like \(J_z\) of spin-1/2 particles.

  3. I am going to have to think about this a bit. The argument is that because particles 1 and 4 are not held as a pair by Alice, Bob or Charlie that they then have no spatial correlation that makes them local. This lack of spatial correlation between these particles is really involved with the state preparation, which here is identified with the portions of the 4-qubit system held by ABC.

  4. I really enjoy the Moldoveanu/Motl banter and encourage you to keep it up despite Motl's obstreperous manner. Seeing two very smart people argue over a very simple thing like quantum causality shows the more simple-minded like myself what a deep rabbit hole science is in today.

    Although it is useful to try to untangle the quantum bonding states of the exchange of light that bonds a source to an observer, you must include the source as well as the observer along with the exchange of a photon. After all, that photon "travels" both ways in the emergent space and time.

    By not including the source along with the exchange and observer, the quantum description is incomplete. Space and time emerge from the superpositions of bonding states of a molecule, which are photon exchanges. Space and time also emerge from the bonding states of any source and observer, but quantum bonds necessarily involve exchanges of identical particles, paths, and times.

    Including the source along with photon exchange and the observer, who by the way is also a source that shines the same photon back to the source, simplifies all of these contortionist quantum superpositions.

    ...but of course, what do I know?

  5. Lubos, long story short. Put Alice, Bob, and Charlie in a big comfortable box. Out of this box only particles 1 and 4 come out. They are entangled any way we desire because when we build the box we wrote instructions for Charlie on a piece of paper telling him to measure 2 an 3 and instructing which pairs of 1 and 4 to let out and which to discard.

    From the outside of the box not knowing the inner workings we keep getting pairs of entangled particles which also never interacted between themselves.

    So your overreaching statement is false, no ifs, ands, buts, or xors.

    1. You, Florin:

      From the outside of the box not knowing the inner workings we keep getting pairs of entangled particles which also never interacted between themselves


      Except that this statement is complete rubbish. They have interacted. If Charlie is picking which pairs 1+4 are allowed to leave the box, the particles 1+4 (or the door that may release them) must wait for Charlie's verdict (whether they should leave or be liquidated inside), and this takes the usual time t = x / c. So the leaving particles 1 and 4 obviously *did* share decisive events in their past light cones - Charlie's decision about their fate! It's this decision of Charlie to open the doors either as open-open or close-close that created the correlation. Because of this extra delay needed to censor things, everything is in perfect agreement with locality again - it always is.

      This is just amazing. Why the hell don't you (Florin) think at least for five minutes before you write additional statements about cases that are clearly even more complex than the simple ones that already exceed your abilities? You're a neverending source of totally wrong assertions and you keep on producing this šit again and again and again and again.

      You would only have a chance to learn quantum mechanics if you actually drew lessons from anything you are doing. The lesson from the previous discussion about the simple swapping without censorship and adjustable paper-written notes is that you were 100% wrong and I was 100% right. But you always keep this *essential* conclusion in someuncertain state so you just recycle all your misconceptions and stupidities in new examples of wrong descriptions of additional situations.

    2. "They have interacted."

      No they did not not. Why is this so hard to comprehend?

      There is a causal chain link between them however, otherwise it would not work but this is not the same as the particle interacting between themselves.

      By the way there is an experiment where particle 1 is long gone before particle 4 is generated. This is like Julius Caesar never interacting with Abraham Lincoln, although they may be correlated in terms of leadership styles through causal chains between them. Or your views being correlated with Trump even though you did not meet.

    3. This comment has been removed by the author.

    4. Your understanding of the basic issues is worse than that of an average physics-liking 10-year-old kid. How the fuck can you say that when a guy decides whether two doors are open, the particles going through the doors do have a common interaction in the past that affected them? Not getting this really means that you're absolutely hopeless. You have *zero* chance to learn any nontrivial physics, ever.

  6. We may have the following nonlocal entanglement swap. Suppose that Alice has particle 1 and 3 and Bob has particle 2 and 4. Alice has particle 3 that is entangled with Bob's state 4, and similarly Bob's state 2 is entangled with Alice's state for particle 1. We now let Alice teleport her state 3 to Charlie and similarly Bob teleports his state 2 to Charlie. Charlie has two states now entangled with both Alice and Bob's state. This is even though Charlie has not interacted with either Alice or Bob. In that case we have particles 2 and 3 held by Charlie entangled with particle 4 and 1 held respectively by Alice and Bob, though there is no prior interaction.

  7. I am still trying to understand the dispute without violation of locality (no FTL).I have one question though.Does your last equation mean that when 1 and 4 are entangled, some (?) entanglement remains in 2 and 3 or one needs more complete calculation to figure out how much entanglement remains in each pair. I believe there are degrees of entanglement.

    1. Kashyap,

      There is actually no dispute on locality/nonlocality. (there will be one when I'll blog about Mr. B socks).

      The last equation shows that when you start you have 1-2 and 3-4 entangled and after the measurement 1-4 and 2-3 become entangled. See my reply above to Lubos. Lubos claimed that in order to create entanglement the two particles ALWAYS need to have interacted in the past. The little calculation in the post shows a counterexample to this too strong a claim: there is a way to create 2 particle entanglement and moreover the 2 particles never interacted in the past. This is all there is to it to this post: a little counterexample which is usually given as a homework problem in quantum information classes.

      I caught Lubos with his pants down but I did not write this post without giving him a fair warning and an opportunity to change his statement. He chose to triple down instead. Why? Either incompetence of brand protection. I don't think he is incompetent, although he is rusty sometimes in QM knowledge. I think this was a "Martha Stewart" moment: recall how she chose to go to jail for inside trading rather than admit she was wrong and in the process destroy her branding image of "perfection".

    2. I have shown in detail why my statement 100% holds and you are 100% wrong. If you *still* don't understand this simple exercise, I strongly urge you to quit attempting doing science or anything that requires a similar brain poser because you have no chance to produce anything besides complete rubbish.

    3. Teleportation of states is a case of nonlocality. If there are no nonlocal properties to quantum states, then it should be possible to teleport states with classical mechanics. Please explain how you propose that would work.

    4. Florin,

      RE the box with Charlie in it: 1-2 and 3-4 are in a mixed state prior to Charlie observing them. Charlie is observing a mixture of 1 and 2 and 3 and 4. That is an interaction of 1 and 4. They are entangled only when they are in the same light cone.

    5. "RE the box with Charlie in it: 1-2 and 3-4 are in a mixed state prior to Charlie observing them. Charlie is observing a mixture of 1 and 2 and 3 and 4. That is an interaction of 1 and 4. They are entangled only when they are in the same light cone."

      Incorrect on three counts:
      - 1 and 4 never interacts
      - 1 and 4 can get entangled even when they are not in the same light cone
      - the condition for entanglement is the existence of the 2 Bell pairs + a joint measurement

  8. Dear Florin and Lubos,

    I have previously presented an argument against the consistency of local non-realism (the position you both support).

    The answer Lubos gave to this argument helped me better understand this position and sharpen the argument. I will present it again here.

    1. Description of the experiment

    a. Two entangeled particles are created at time T0.

    b. One of the particles (P2) is sent in a distant place. It arrives there at T1. The other one (P1) remains in the lab. Bob writes down his opinion about the spins’ existence.

    c. Bob measures the spin of P1 on Z. at time T3

    d. At some time after measurement (T4) Bob writes down again his opinion about the spins’ existence.

    Lubos maintains that Bob’s first statement (S1) written at time T1 and Bob’s second statement (S2) written at time T4 are both true. Let’s write them here:

    S1: The spins do not exist, they will be created at the time of the measurement. (non-local non-realism)

    S2: The spins existed before the measurement. Just like in the case of Bertlmann's socks the measurement revealed their pre-existing values. (local realism).

    One can easily see that there is no way S1 and S2 can both be true. Lubos arrived at a contradiction but he doesn’t have the courage to take the required action, reject either S1 or S2. He tries to escape the inevitable by complaining that I have used different observers, perspectives, histories, whatever. It can be seen that this is not the case. We have one observer (Bob), one experiment, one measurement, one history. And still, the two accounts of this one observer are contradicting each other. This is not a case of complementary either. We don’t combine two or more measurements, only one takes place.


    To be continued (text too large)

  9. Continued from the previous post:

    To make an analogy, let’s say an alleged witness in a murder trial is interrogated by both the prosecutor and defense. He gives the following answers:

    To prosecution: I have seen the accused killing the victim with a knife.

    To defense: I have seenn nothing, I couldn’t because I was 1000 Km away.

    Asked again by the prosecution he confirms that everything he said is true and he sees no contradiction at all. If not proven insane, the witness will spend a lot of time in jail.

    Ok, let’s develop the argument further by choosing locality (S2) over non-realism (S1). After all, there is plenty evidence for locality but no evidence for non-realism. Here Lubos thinks there is a problem because, if Bob changes his mind at T1 and measures the spin on X or on Y he should ascribe reality to all spin components leading to a contradiction with the experimental results as Bell’s theorem shows. This implication is true so we have to choose between:

    S2: The spins existed before the measurement. Just like in the case of Bertlmann's socks the measurement revealed their pre-existing values. (local realism).

    S3: The experimenter has free-will (he can change his mind) (non-determinism)

    This choice is easy again. There is no good evidence for free will so it has to be rejected. And, as a bonus, Bell’s theorem goes down the drain too (no free-will, no theorem). So we can actually ascribe reality to all spin components and we are free of all contradictions.

    So, until now, I have proven that realism + determinism must be true if locality is true. No other assumptions have been made. Einstein was right. Bohr was wrong. There is no doubt about it. QM is incomplete and non-fundamental. This is probably the explanation why quantizing gravity is so hard.

    I have noticed that Lubos included a small paragraph about ER=EPR. Are you serious Lubos? Wormholes? Why are you not making the obvious choice here and start exploring some local realist theories like stochastic electrodynamics? It might help you get a free ticket to Stockholm after all.

    Now, this argument was not about entanglement swapping but it is important to argue from a correct position. A mistake that is repeated here is that there is such a thing as non-interacting particles in this experiment. The particles must get close together to speak about an interaction. This billiard-ball model obsession never seems to die. As both classical and quantum electromagnetism show, all charged particles interact all the time by means of the fields generated by them. It does not matter if they are far or close (after all this far/close distinction is ill-defined. If you take Plank length as the fundamental scale, an electron is very far away from a proton in a hydrogen atom and nobody will claim that there is no interaction.). So, there is no question of non-locality here. All of the particles involved did interact in the past.


    1. Curiously ER = EPR is a great case for nonlocality. The black hole with a split horizon at the origin is an entanglement of black holes in two regions. Hawking radiation can shift the entanglement form the black holes to the different regions. The horizon is no longer split and does not meet. In this way we may think of spacetime as made up of entanglements.

      Teleportation is a case of quantum nonlocality. Of course the structure of these entanglement swaps is a form of LOCC that tells you what classical signal is needed to read the teleported state. However, you can't teleport classical states, and if Lubos can show how it can be done he might become actually famous instead of notorious.

      Lubos' arguments all amount to classical logic, and he is assuming that this can be understood by classical reasoning, which in some sense is why is makes his conclusions. It is odd to be revisiting this subject, for everyone from Bohr, who argued with Einstein on just this matter with right and left gloves instead of colored socks, on down has concluded quite to the contrary of Lubos.

    2. "Lubos' arguments all amount to classical logic"

      Indeed and I will battle it in due time. For now however the dispute is on a simple fact: can you produce entangled particles which never interacted in the past: yes or no?

      If yes then I am right and Lubos is wrong
      If no then I am wrong and Lubos is right.

    3. If J_z is the only property of the 4 spins that is ever measured, the entanglement works along *identical* rules to classical correlations of e.g. Bertlmann's socks, and that's why the discussion and explanations of all the correlations in these quantum experiments and their relationship with locality and causation are *identical* to the classical correlations, e.g. Bertlmann's socks.

      It's absurd that ER=EPR supports nonlocality. Just search for the word "locality" in arXiv:1306.0533, the ER=EPR paper. You will find some 10 hits. A big part of the paper - a key point of it - is explaining why locality isn't violated. For example, the paper starts with:

      Spacetime locality is one of the cornerstones in our present understanding of physics. By locality we mean the impossibility of sending signals faster than the speed of light. Locality appears to be challenged both by quantum mechanics and by general relativity. Quantum mechanics gives rise to Einstein Podolsky Rosen (EPR) correlations [1], while general relativity allows solutions to the equations of motion that connect far away regions through relatively short “wormholes” or Einstein Rosen bridges [2]. It has long been understood that these two effects do not give rise to real violations of locality. One cannot use EPR correlations to send...

      Maldacena and Susskind explain that the "violations of locality" in both pictures, GR and QM, are just apparent and no violation of locality ever emerges.

    4. There is no violation of locality in that no information is communicated faster than light. There is no signal communication faster than light. However, nonlocality in the QM sense can't itself be reduced to locality,

  10. Andrei,

    Not sure how you arrived at S1 and S2. The spins do not exist before measurement but once measured, a subsequent measurement will reconfirm the value. Not sure where you see a contradiction with this.

    If the values are always there then you can show the necessity of Boolean logic to argue consistently about them. If the measurement values are created as a result of measurement then you can prove the necessity of the logic of projection operators in a Hilbert space to argue consistently (This is not hanwaving, there are papers written on this which shows how in a constructive way).

    Local realism demands Kolmorogov theory, while QM demands the existence of a Hilbert space and the logic of projection operators in a Hilbert space. Both cases are consistent because both classical physics and quantum mechanics are self-consistent theories. However only one of them can describe nature correctly and this is QM.

    1. Florin,

      "Not sure how you arrived at S1 and S2"

      I have tailored the argument against Lubos'position, sorry if that was not clear. Nevertheless, S1 and S2 are the only possibilities available to explain the observed correlations. The spins are created at the time of measurement or they are not created at that time (they existed before).

      The argument is simple. If you go with S1 you have non-locality. It is a kind of non-locality that cannot be used to send a signal because you cannot controll the result of the measurement (Lubos claimed that any non-locality can be used to send a signal, so he is wrong on this one too). S2 is the local-realistic point of view.

      Now, Lubos wants the best of both worlds. He wants the non-realism of S1 (because he believes in free-will or whatever non-scientiffic reason) and the locality of S2. He is not merely saying that the spins did not exist before measurement but they do afterwards. He is saying that untill the measurement takes place, the spins do not exist, but after the measurement you can say, after all, that they existed even before the measurement. This is the contradiction. He wants to have two contradictory accounts for the same situation (the state of spins before measurement).

      As far as I can tell from your post, you go with S1 so you agree that physics is non-local. So, it seems to me Lubos was right to accuse you of pushing non-local ideas.


    2. Andrei,

      S1 does not imply nonlocality, but nonrealism. Guilty of that :)

    3. Florin:

      "S1 does not imply nonlocality, but nonrealism"

      It does not imply non-locality for the particle that is measured, but implies non-locality for the distant particle. You measure one particle here and you create the value of the spin for both entangled particles (including the one that is far away).


  11. Lubos you are more stubborn than a mule. If you put the 3 people in a box you can generate entangled particles which never interacted. Use photons instead of electrons and keep them circulating in two fiber optics loops until Charlie decides to release them outside the box or not. From their birth the two photons never interacted, and while in the loop they continue not interacting. Viewed from outside the box produces at random times pairs of entangled photons which never interacted.

    1. If two particles are released by Charlie when they have the same property, and not released when they have the opposite property, then obviously both of these particles are being affected by the same interaction in their shared past light cone - the thinking processes in Charlie's brain.

      I have explained this trivial thing just on this thread about 4 times. A smart kid would get it after the 1st explanation.

      Is it surprising for you that a person who can cherry-pick pairs can introduce a correlation for the survivors? Is this "miracle" what encourages you to believe in your other nonlocality miracles? Cherry-picking or filtering is the process that is producing many/most correlations in the most general situations.

      The information isn't carried just by the particles. It's also carried by the door that may open and release them or not, and the wires that control these doors. It's this information that you completely overlook that is critical and where the correlation is created. All this information that decides about the subsequent correlation always propagates by the speed of light and every correlation always has events in the shared light cones of the relevant objects that fully explain this correlation.

    2. no , it is not obvious at all . filtering out particles does not automatically create interaction between particles. I start to believe Lubos is masking his incompetence by vulgarity.

    3. "filtering is the process that is producing many/most correlations in the most general situations."

      BINGO: you just contradicted yourself.

      Yes, filtering under appropriate conditions do produce correlations and this contradicts your overreaching incorrect statement: "Whenever there's some correlation in the world – in our quantum world – it's a consequence of the two subsystems' interactions (or common origin) in the past.".

      This is the point of the post: interaction between particles is not ALWAYS needed to produce correlations.

    4. Filtering doesn't produce correlations "automatically" i.e. always but it obviously creates correlations in this case - and most others.

      Charlie is simply releasing the pair when their properties are the same, and otherwise kills them. How could you question that the filtering is the *reason* for the correlation? You must be not just an obnoxious anonymous troll but a complete imbecile not to understand this.

    5. Put the beer down and read carefully what I said: "Yes, filtering under appropriate conditions do produce correlations"

      "How could you question that the filtering is the *reason* for the correlation?" I am not. Please comment when you are not drunk.

    6. Florin Moldoveanu: Put the beer down and read carefully what I said: "Yes, filtering under appropriate conditions do produce correlations"

      Excellent. Now, the filtering is caused by the decision in Charlie's brain which is in the intersection of the two past light cones of events -measurements of particles 1,4, right?

      So you haven't found any counterexample to my statement, have you?

    7. BTW my nation is the #1 drinker of beer and I am not avoiding ethanol in any systematic way but I am in no way a major drinker.

      In average, and almost regularly, I drink 0.5 liters of beer that has about 4% of ethanol in average. That's about 20 ml of ethanol a day in average. None of it was drunk in the vicinity of 1 hour around the moments when I was writing replies. This 1 hour is enough for the 20 ml of ethanol to get almost entirely out of the blood system.

      Beer is mostly healthy in normal enough amounts.

    8. I like Pilsen beer by the way.

      "Charlie's brain which is in the intersection of the two past light cones of events -measurements of particles 1,4, right?"

      -WRONG. At the time of measuring 2 and 3 by Charlie, his brain could be outside the intersection of the past light cone of the 1 and 4 measurements. Let me try drawing it here. Assume the lines are at 45 degrees and we are dealing with Bell pairs of photons

      ( (
      ) )
      ( (
      A1 C B4
      2 3
      \ /\ /\
      \ / \ / \
      1\/2 3\/4 \
      /\ /\
      / \ / \
      / \/ \

      The dotted line is the intersection of the past light cones of the Alice and Bob measurements (A1 and B4). The measurement event by Charlie is C23 and is above the light cone intersection. After measurement by Alice and Bob the photons are stored in a cavity bouncing back and forth mirrors (or stored in a fiber optics loop) and they cannot interact anymore. Time needs to pass from the moment Charlie makes the measurement for his decision to reach the fiber loops to release or not the photons.

    9. Drawing is messed up, now I have to write another post with the proper picture to explain it.


  12. Lubos, one more thing. You wrote a post: "Entanglement swapping doesn't violate locality" For the record I never claimed that it does.

    1. Of course you have. This whole blog post above is that my propositions - which are *defining* what locality means - are violated.

  13. There is one thing for which most physicists would agree is Lorentz Invariance (no FTL) which is called 'locality' by many people. So let us agree on that first and then proceed further! I thought particles 2 and 3 are sent to Charlie for Bell type measurement which entangles them. I do not understand why Charlie has control over 1 and 4 which are really under control of Alice and Bob.I guess one has to understand how experiment is done. Perhaps Zeilinger(if my recollection is right), father of such experiments, can weigh on this.Is it possible to invite him to write a comment or guest blog? I am sure he will not question Lorentz invariance, but he can resolve other issues.

  14. I forgot to mention one thing. Is this a matter of delayed choice where 2 and 3 interact in future, but affect 1 and 4 which happened in past?

    1. Excellent question: The past is the past and cannot be changed, However one can discover correlations about events in the past. But the story is subtle. Charlie's measurement can have one of 4 outcomes. In 25% of the cases one uncovers the past correlation. The one in 4 cases is itself a random outcome. Think of Charlie result of measurement as the key to unlock the correlation which otherwise would remain hidden.

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    3. Ok! I now see that this picking of 1 of 4 outcomes is what you guys are calling filtering.So the other three do not result in entanglement of 1 and 4. Now I am even more curious about Zeilinger's or someone else's set up for swapping or teleportation.I guess the devil is in details!

    4. That was what I wrote about the other day. Particles 1 and 4 can be a correlated through teleportation, which does not require a direct interaction of the particles. As I said, teleportation is a case of nonlocality and it is not something in classical mechanics.

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  15. Lawrence Crowell,
    Ok!I did not see it at that time.But now this is becoming clearer.What are locality and non-locality, is a matter of furious debate!Many people (specially Lubos) take locality as synonymous with Lorentz invariance. I am mostly with him on that issue. e.g. our usual field theory is called local field theory.As I mentioned once before, Bell unfortunately used the word non locality for non-factorizability. I am not sure if you and/or Florin use the word 'non-locality'in the same sense or have deeper meaning in mind. It seems that both of you believe in Lorentz invariance. So I would like to understand your 'non-locality' better. Is it a matter of semantics only or not?

    1. I think there is some relationship, maybe a duality, between symmetries that are nonlocal and those that are local, or that define causal processes by light cone condition, time ordering etc. If so this would remove a vast number of local symmetries or amplitudes from the real physics.

      Lorentz invariance is a pretty strong bedrock. If spacetime is built up from entanglement then Lorentz invariance is a manifestation of QM in some manner. If so there is then some relationship between nonlocal and local physics. Something very subtle lies here.

      Nonlocal physics does not violate causality or locality. Nonlocality does not involve causal influences or the transmission of information along spacelike intervals. Even when there is a nonlocal correlation this can only be realized to an observer through the transmission of a classical signal. This converts an entangled state, say a state involving two spins that has no ontological meaning to those component spins, into the nonentangled state where the qubit content of the entangled state is transferred to the new form as component spins.

      I am a bit curious about what Lubos is claiming, and so far he has not illustrated how teleportation of states can occur classically. He is not always right about things. I checked his blog recently where he states that regions of Asia and Africa were maybe better off under the European empires. That is a bit of a long claim.