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Mathematics 2016, 4(3), 48; doi:10.3390/math4030048

Sharing of Nonlocality of a Single Member of an Entangled Pair of Qubits Is Not Possible by More than Two Unbiased Observers on the Other Wing

1
S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
2
Center for Astroparticle Physics and Space Science, Bose Institute, Kolkata 700091, India
*
Author to whom correspondence should be addressed.
Academic Editors: Paul Busch, Takayuki Miyadera and Teiko Heinosaari
Received: 27 April 2016 / Revised: 5 July 2016 / Accepted: 6 July 2016 / Published: 16 July 2016
(This article belongs to the Special Issue Mathematics of Quantum Uncertainty)
View Full-Text   |   Download PDF [717 KB, uploaded 16 July 2016]

Abstract

We address the recently posed question as to whether the nonlocality of a single member of an entangled pair of spin 1 / 2 particles can be shared among multiple observers on the other wing who act sequentially and independently of each other. We first show that the optimality condition for the trade-off between information gain and disturbance in the context of weak or non-ideal measurements emerges naturally when one employs a one-parameter class of positive operator valued measures (POVMs). Using this formalism we then prove analytically that it is impossible to obtain violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality by more than two Bobs in one of the two wings using unbiased input settings with an Alice in the other wing. View Full-Text
Keywords: quantum measurement; POVM; unsharp measurement; nonlocality quantum measurement; POVM; unsharp measurement; nonlocality
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Mal, S.; Majumdar, A.S.; Home, D. Sharing of Nonlocality of a Single Member of an Entangled Pair of Qubits Is Not Possible by More than Two Unbiased Observers on the Other Wing. Mathematics 2016, 4, 48.

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