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arXiv:quant-ph/0507189 · Physical Review A

Single-particle entanglement

S. J. van Enk

Published Dec 29, 2005• 212 citations
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Abstract

I give a simple argument that demonstrates that the state $\ensuremath{\mid}0⟩\ensuremath{\mid}1⟩+\ensuremath{\mid}1⟩\ensuremath{\mid}0⟩$, with $\ensuremath{\mid}0⟩$ denoting a state with 0 particles (or photons) and $\ensuremath{\mid}1⟩$ a one-particle state, is entangled in spite of recent claims to the contrary. I also discuss viewpoints on the old controversy about whether the above state can be said to display single-particle or single-photon nonlocality.

DOI
10.1103/physreva.72.064306

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I try to rebut Drezet's arguments [Phys. Rev. A. 74, 026301 (2006)]) against the state $\ensuremath{\mid}0⟩\ensuremath{\mid}1⟩+\ensuremath{\mid}1⟩\ensuremath{\mid}0⟩$ being entangled by agreeing with them. I also address some old arguments repeated by Drezet.

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Comment on “Single-particle entanglement”

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Single-particle entanglement

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I give a simple argument that demonstrates that the state \ensuremath∣0⟩\ensuremath∣1⟩+\ensuremath∣1⟩\ensuremath∣0⟩\ensuremath{\mid}0⟩\ensuremath{\mid}1⟩+\ensuremath{\mid}1⟩\ensuremath{\mid}0⟩\ensuremath∣0⟩\ensuremath∣1⟩+\ensuremath∣1⟩\ensuremath∣0⟩, with \ensuremath∣0⟩\ensuremath{\mid}0⟩\ensuremath∣0⟩ denoting a state with 0 particles (or photons) and \ensuremath∣1⟩\ensuremath{\mid}1⟩\ensuremath∣1⟩ a one-particle state, is entangled in spite of recent claims to the contrary. I also discuss viewpoints on the old controversy about whether the above state can be said to display single-particle or single-photon nonlocality.
We propose a single-particle experiment that is equivalent to the conventional two-particle experiment used to demonstrate a violation of Bell's inequalities. Hence, we argue that quantum mechanical nonlocality can be demonstrated by single-particle states. The validity of such a claim has been discussed in the literature, but without reaching a clear consensus. We show that the disagreement can be traced to what part of the total state of the experiment one assigns to the (macroscopic) measurement apparatus. However, with a conventional and legitimate interpretation of the measurement process one is led to the conclusion that even a single particle can show nonlocal properties.
There has been a great deal of debate surrounding the issue of whether it is possible for a single photon to exhibit nonlocality. A number of schemes have been proposed that claim to demonstrate this effect, but each has been met with significant opposition. The objections hinge largely on the fact that these schemes use unobservable initial states and so, it is claimed, they do not represent experiments that could actually be performed. Here we show how it is possible to overcome these objections by presenting an experimentally feasible scheme that uses realistic initial states. Furthermore, all the techniques required for photons are equally applicable to atoms. It should, therefore, also be possible to use this scheme to verify the nonlocality of a single massive particle.
A recent paper "Single-world interpretations of quantum theory cannot be self-consistent" [arXiv:1604.07422] by D. Frauchiger and R. Renner has attracted a considerable interest of a broader physics audience and shortly elicited a number of replies. In spite of the objections that ensued, we find that significant part of the controversial initial claim has not been refuted - on the contrary, arguments presented both in the initial paper and in the replies seem to leave no longer room for the basic Copenhagen interpretation of quantum mechanics. We revisit the controversy trying to pinpoint the exact phenomenon that lies in its core, pointing out to some aspects of the problem that seem to have been mostly overlooked. Taking all conclusions into account, we here propose novel ways to approach the ostensible paradox, in which the Copenhagen interpretation is naturally preserved. Whereas arguments presented in Frauchiger and Renner paper and the replies that followed revolve over whether Wigner's friend would perceive only one or both of the possible outcomes, we offer the third, pretty obvious solution - namely, that Wigner's friend, in the well known setup, would subjectively perceive {\it none} of the potentially conflicting outcomes. As a side note, we also argue that, contrary to the often stated beliefs, hypothetical real experimental realization of Wigner's friend thought experiment actually would not provide us with any new insight into the quantum mechanics.