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

Shiladitya Mal, Archan S. Majumdar and Dipankar Home
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Shiladitya Mal: S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
Archan S. Majumdar: S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
Dipankar Home: Center for Astroparticle Physics and Space Science, Bose Institute, Kolkata 700091, India

Mathematics, 2016, vol. 4, issue 3, 1-9

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.

Keywords: quantum measurement; POVM; unsharp measurement; nonlocality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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