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International Journal of Quantum Information

CLASSICAL PROTOCOL FOR SIMULATION OF SPIN MEASUREMENT CORRELATIONS OF BINARY SPIN-S SINGLET STATE

Ali Ahanj, Pramod S. Joag, Sibasish Ghosh A

Published Jun 1, 2010• 0 citations
Publisher

Abstract

In a recent paper [A. Ahanj et al., Phys. Lett. A368 (2007) 34], we gave a classical protocol to simulate quantum correlations corresponding to the spin-s singlet state for the infinite sequence of spins satisfying 2s + 1 = 2n. In the present paper, we have generalized this result by giving a classical protocols to exactly simulate quantum correlations implied by the spin-s singlet state corresponding to all integer as well as half-integer spin values s. The class of measurements we consider here are only those corresponding to spin observables, as has been done in the above-mentioned paper. The required amount of communication is found to be ⌈ log 2(s + 1)⌉ in the worst case scenario, where ⌈x⌉ is the least integer greater than or equal to x.

DOI
10.1142/s0219749910006423

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Simulation of two spin-sss singlet correlations for all sss involving spin measurements
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We give a classical protocol to exactly simulate quantum correlations implied by a spin sss singlet state for the infinite sequence of \textit{integer} spin s=1,4,13,...s={1,4,13,...}s=1,4,13,... satisfying (2s+1)=3n(2s+1)=3^{n}(2s+1)=3n,where nnn is a positive integer.The required amount of communication is found to increase as log3d2log_{3}d^{2}log3​d2 where d=2s+1d=2s+1d=2s+1 is the dimension of the spin sss Hilbert space.
Recent work has extended Bell's theorem by quantifying the amount of communication required to simulate entangled quantum systems with classical information. The general scenario is that a bipartite measurement is given from a set of possibilities and the goal is to find a classical scheme that reproduces exactly the correlations that arise when an actual quantum system is measured. Previous results have shown that, using local hidden variables, a finite amount of communication suffices to simulate the correlations for a Bell state. We extend this in a number of ways. First, we show that, when the communication is merely required to be finite on average, Bell states can be simulated without any local hidden variables. More generally, we show that arbitrary positive operator valued measurements on systems of n Bell states can be simulated with O(n2n){O(n2}^{n})O(n2n) bits of communication on average (again, without local hidden variables). On the other hand, when the communication is required to be absolutely bounded, we show that a finite number of bits of local hidden variables is insufficient to simulate a Bell state. This latter result is based on an analysis of the nondeterministic communication complexity of the NOT-EQUAL function, which is constant in the quantum model and logarithmic in the classical model.
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