Nonlocal aspects of a quantum wave

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 5, 2000, Pages 521081-5210811

  Aharonov, Y ^a,b   Vaidman, L ^a  

^a TEL AVIV UNIVERSITY   (Israel)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346481054     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

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27. While in the past one of us [28] disagreed with the use of the term "single-photon nonlocality" today it has become an accepted term, and it fits well the context of the present paper. The objection was that the name is misleading because it appeared shortly after the three-particle nonlocality of the Greenberger-Horne-Zeilinger-(Mermin) [18,19] example and the two-particle nonlocality of Hardy's example [29]. The present nonlocality is not a one-particle nonlocality in the sense of these papers.
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33. Although we did not mention "coherent state" in the gedanken experiment of finding the phase φ of a single photon state through swapping it to the state of the pair of spin-1/2 particles, the analog of the coherent state was present in that case too. The ability to measure a spin component in an arbitrary direction requires a reference frame for the direction in space. The quantum state with a well defined angle is a superposition of different angular momentum states, which is analogous to the superposition of different number states in the coherent state of photons.
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37. One might naively object to this argument in the following way: An electron and a positron cannot annihilate to a single photon by themselves. They have to transfer momentum to another body. Thus, what we will get is the photon in A and a body in A with shifted momentum in a superposition with the photon in B and the body in B with shifted momentum. If the states of the bodies with and without the shift of momentum are orthogonal, then we do not get the pure photon state (34) but a mixture. However, we can (and must) arrange the initial states of the bodies that take part in the annihilation process so that the uncertainty in momentum is much larger than the mo-mentum recoil.
38. We should not confuse it with entanglement swapping, which is usually used in the context of two entangled pairs AB and CD with measurement performed on the pair BC which generates entanglement between A and D [39]. Here we discuss swapping of a different type: both before and after the swapping the entanglement is between the same sites A and B.
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