Logical pre- and post-selection paradoxes are proofs of contextuality

TY - GEN

T1 - Logical pre- and post-selection paradoxes are proofs of contextuality

AU - Pusey, Matthew F.

AU - Leifer, Matthew S.

PY - 2015/11/5

Y1 - 2015/11/5

N2 - If a quantum system is prepared and later post-selected in certain states, "paradoxical" predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective measurement with Luders-von Neumann update rule, or with weak measurements where they show up in anomalous weak values. Leifer and Spekkens [quant-ph/0412178] identified a striking class of such paradoxes, known as logical pre- and post-selection paradoxes, and showed that they are indirectly connected with contextuality. By analysing the measurement-disturbance required in models of these phenomena, we find that the strong measurement version of logical pre- and post-selection paradoxes actually constitute a direct manifestation of quantum contextuality. The proof hinges on under-appreciated features of the paradoxes. In particular, we show by example that it is not possible to prove contextuality without Luders-von Neumann updates for the intermediate measurements, nonorthogonal pre- and post-selection, and 0/1 probabilities for the intermediate measurements. Since one of us has recently shown that anomalous weak values are also a direct manifestation of contextuality [arXiv:1409.1535], we now know that this is true for both realizations of logical pre- and post-selection paradoxes.

AB - If a quantum system is prepared and later post-selected in certain states, "paradoxical" predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective measurement with Luders-von Neumann update rule, or with weak measurements where they show up in anomalous weak values. Leifer and Spekkens [quant-ph/0412178] identified a striking class of such paradoxes, known as logical pre- and post-selection paradoxes, and showed that they are indirectly connected with contextuality. By analysing the measurement-disturbance required in models of these phenomena, we find that the strong measurement version of logical pre- and post-selection paradoxes actually constitute a direct manifestation of quantum contextuality. The proof hinges on under-appreciated features of the paradoxes. In particular, we show by example that it is not possible to prove contextuality without Luders-von Neumann updates for the intermediate measurements, nonorthogonal pre- and post-selection, and 0/1 probabilities for the intermediate measurements. Since one of us has recently shown that anomalous weak values are also a direct manifestation of contextuality [arXiv:1409.1535], we now know that this is true for both realizations of logical pre- and post-selection paradoxes.

U2 - 10.4204/EPTCS.195.22

DO - 10.4204/EPTCS.195.22

M3 - Conference contribution

T3 - Electronic Proceedings in Theoretical Computer Science

SP - 295

EP - 306

BT - Proceedings of the 12th International Workshop on Quantum Physics and Logic

A2 - Heunen, Chris

A2 - Selinger, Peter

A2 - Vicary, Jamie

ER -