bibkey: choudhary2013temporalhardy
authors: Sujit K. Choudhary; Sandeep K. Goyal; Thomas Konrad; Sibasish Ghosh
year: 2013
title: "Persistence of Hardy's nonlocality in time"
doi: null
url: https://arxiv.org/abs/1302.5296v1
claim: "For the temporal version of Hardy's argument on a single d-level system with projective measurements, the paper proves that the success probability is at most 1/4 in every dimension, shows that spin-1 and spin-3/2 spin measurements attain it, and conjectures that the maximum 1/4 can be observed for any spin system."
strata_touched:
  - D5/S3/Quantum/Contextuality/TemporalHardySpinAttainment
license: citation-only
triage: anchor

Persistence of Hardy’s nonlocality in time

Sujit K. Choudhary, Sandeep K. Goyal, Thomas Konrad and Sibasish Ghosh, arXiv:1302.5296v1 (quant-ph), 2013-02-21. Quotations are from the v1 TeX source.

The experiment (Section II):

Consider a single $d$ level physical system on

which an observer (Alice) chooses to measure one of two observables ${\hat{A}}_1$ or ${\hat{A}}_2$ at time $t_1$, whereas at a later time $t_2$, another observer (Bob) \cite{bob} measures either of the two observables ${\hat{B}}_1$ and ${\hat{B}}_2$.

The conditions in quantum mechanics (Section III):

&{\rm prob}(\hat{A}_1,a_1 ; \hat{B}_1,b_1)=\langle \psi

|\Pi_{a_1,{A_{1}}}\Pi_{b_1,{B_{1}}}\Pi_{a_1,{A_{1}}}|\psi\rangle=0,& \label{eqn-1a}\

&{\rm prob}(\hat{A}_2,a_2; \hat{B}_2,b_2) =\langle \psi

|\Pi_{a_2,{A_{2}}}\Pi_{b_2,{B_{2}}}\Pi_{a_2,{A_{2}}}|\psi\rangle > 0. \label{eqn-4a}

The conjecture (Conclusion and Appendix B):

can also be achieved. Moreover, we conjecture that this maximum can be observed for any spin system.

We conjecture that the maximum of the success probability appearing in the temporal version of Hardy’s

argument is $25\%$ for any spin-$s$ system. We write below the state and observable setting which

Verified locator

• URL: https://arxiv.org/abs/1302.5296v1 (v1, 2013-02-21; source choudhary.tex, md5 e163b7fd286cb4b9973a4f0479f21807): the experiment (l. 111–123), the quantum conditions (l. 154–186), the conclusion (l. 386–390) and Appendix B (l. 586–590).
• The conjecture is repeated in S. K. Choudhary and P. Agrawal, Int. J. Quantum Inf. 14 (2016) 1640035, arXiv:1610.01152, §9. That text was not quoted here.