Conservation of correlation in measurement underlying the violation of
Bell inequalities and a game of joint mapping
- URL: http://arxiv.org/abs/2208.03441v1
- Date: Sat, 6 Aug 2022 04:20:48 GMT
- Title: Conservation of correlation in measurement underlying the violation of
Bell inequalities and a game of joint mapping
- Authors: Agung Budiyono
- Abstract summary: We show that it is the requirement of conservation of correlation which compels quantum measurement to violate the Bell inequalities.
A quantum strategy with an access to an ensemble of entangled spin-$frac12$ particles and circuits for local quantum spin measurement, can be used to win the game.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: What compels quantum measurement to violate the Bell inequalities? Suppose
that regardless of measurement, one can assign to a spin-$\frac{1}{2}$ particle
(qubit) a definite value of spin, called c-valued spin variable, but, it may
take any continuous real number. Suppose further that measurement maps the
c-valued spin variable from the continuous range of possible values onto the
binary standard quantum spin values $\pm 1$ while preserving the bipartite
correlation. Here, we show that such c-valued spin variables can indeed be
constructed. In this model, one may therefore argue that it is the requirement
of conservation of correlation which compels quantum measurement to violate the
Bell inequalities when the prepared state is entangled. We then discuss a
statistical game which captures the model of measurement, wherein two parties
are asked to independently map a specific ensemble of pairs of real numbers
onto pairs of binary numbers $\pm 1$, under the requirement that the
correlation is preserved. The conservation of correlation forces the game to
respect the Bell theorem, which implies that there is a class of games no
classical (i.e., local and deterministic) strategy can ever win. On the other
hand, a quantum strategy with an access to an ensemble of entangled
spin-$\frac{1}{2}$ particles and circuits for local quantum spin measurement,
can be used to win the game.
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