Comment on "Relativity of Quantum States in Entanglement Swapping: Violation of Bell's Inequality with no Entanglement"
aa r X i v : . [ qu a n t - ph ] F e b Comment on “Relativity of quantum states inentanglement swapping: Violation of Bell’sinequality with no entanglement”(arXiv:1806.02407v2 [quant-ph]; Physics LettersA, Volume 384, Issue 15, 29 May 2020)
Luiz Carlos Ryff
Instituto de F´ısica, Universidade Federal do Rio de Janeiro,Caixa Postal 68528, 21041-972 Rio de Janeiro, Brazil
E-mail: ryff@if.ufrj.brFebruary 9, 2021
Abstract
In a recent interesting article Chris Nagele, Ebubechukwu O. Ilo-Okeke, Peter P. Rohde, Jonathan P. Dowling, and Tim Byrnes discussan entanglement swapping experiment using ”a setup where it is possi-ble to switch the time ordering of measurements.” I would like to drawyour attention to the fact that the very same idea was introduced in twoprevious papers, and briefly address some important points related to thesubjectKey words: EPR correlations; entangled states; Bell’s inequality; spe-cial relativity
In a recent paper Chris Nagele, Ebubechukwu O. Ilo-Okeke, Peter P. Ro-hde, Jonathan P. Dowling, and Tim Byrnes discuss the “Relativity of quantumstates in entanglement swapping” [1]. According to the authors, the differenceof their scenario to past works “is that the order of the measurements dependsupon the reference frame, due to relativity of simultaneity.” They also emphasizethat “Other works have investigated special relativistic effects on entanglementswapping and on teleportation, but none have considered a setup where it ispossible to switch the time ordering of measurements.” In fact, the very samesubject was addressed in two previous papers, entitled “Einstein, Podolsky, andRosen correlations, quantum teleportation, entanglement swapping, and specialrelativity” [2], and “Quantum teleportation and entanglement swapping viewedfrom different moving frames” [3], respectively. In these two papers we have anexperiment which can be seen as being on ordinary Einstein-Podolsky-Rosen1orrelations, on quantum teleportation, or on entanglement swapping, depend-ing on the Lorentz frame we use to observe it. Further, according to Nagele andcoauthors, “In a moving frame, the order of the measurements is reversed, anda Bell violation is observed even though the particles are not entangled, directlyor indirectly, or at any point in time”. Actually, the situation they consideris analogous to the one considered in another paper [4] following a suggestionby Peres [5]. In fact, as has been shown in ref. [3] and [6], there is a simpleexplanation for this apparently mysterious fact. The point is that wheneverthe polarizations are measured first (“polarization analysis”), the two remain-ing photons are projected into well-defined polarization states. Consequently,when they arrive at the beam splitter we will perform an experiment (“Bell-state analysis”) similar to the one performed by Hong, Ou, and Mandel [7], butin which the photons can have different polarizations. Since the probability ofcoincident/non-coincident detection depends on the relative polarization of thephotons, by selecting the events in which we have coincidence/no-coincidence,we obtain a subset that behaves as if it consisted of entangled pairs of distantparticles. The point is that the probability of coincident/no-coincident detec-tion will depend on the experimental outcome at the polarizers. Therefore,nothing paradoxical or more mysterious than quantum nonlocality itself needsto be invoked.Experiments for which different interpretations are possible, depending onthe Lorentz frame we use to describe them, raise the question of what thecorrect interpretation would be, or even whether it would make sense to ask thatquestion. Related to this point, it is interesting to consider situations involvingtime-like events. As was emphasized, in this case there is strong evidence thata measurement performed on one of the photons of an entangled pair changesthe state of the other [8], in other words, there seems to be an undeniable causeand effect relationship. As this influence must still be present when space-likeevents are considered, since the very same correlations can be observed, the ideaentertained by Bohm and Bell [9] that there must be a preferred frame does notsound so preposterous. A way of trying to make this idea compatible with theLorentz transformations is to assume that the Lorentz symmetry is broken inthe case of quantum non-locality [8], namely, there would be no equivalencebetween active and passive Lorentz transformations.
References [1] Chris Nagele, Ebubechukwu O. Ilo-Okeke, Peter P. Rohde, Jonathan P.Dowling, Tim Byrnes, “Relativity of quantum states in entanglementswapping,” Physics Letters A, Volume , Issue 15, (29 May 2020);arXiv:1806.02407v2 [quant-ph].[2] Luiz C. Ryff, “Einstein, Podolsky, and Rosen correlations, quantum telepor-tation, entanglement swapping, and special relativity,” Phys. Rev. A, ,5083 (1999). 23] Luiz C. Ryff, “Quantum teleportation and entanglement swapping viewedfrom different moving frames,” JOURNAL OF MODERN OPTICS, VOL.48