In this paper we present a new approach for testing QM against the realism aspect of hidden variable theory (HVT). We consider successive measurements of non-commuting operators on a input spin
s state. The key point is that, although these operators are non-commuting, they act on different states so that the joint probabilities for the outputs of successive measurements are well defined. We show that, in this scenario HVT leads to Bell type inequalities for the correlation between the outputs of successive measurements. We account for the maximum violation of these inequalities by quantum correlations by varying spin value and the number of successive measurements. Our approach can be used to obtain a measure of the deviation of QM from realism say in terms of the amount of information needed to be transferred between successive measurements in order to classically simulate the quantum correlations.
In this paper, we consider a hidden variable theoretical description of successive measurements of non-commuting spin observables on an input spin-s state. Although these spin observables are non-commuting, they act on different states, and so the joint probabilities for the outputs of successive measurements are well-defined. We show that, in this scenario, hidden variable theory (HVT) leads to Bell-type inequalities for the correlation between the outputs of successive measurements. We account for the maximum violation of these inequalities by quantum correlations (i.e. the correlations of successive measurements on a quantum state) by varying the spin value and the number of successive measurements. Our approach can be used to obtain a measure of the deviation of Quantum Mechanics from the theory obeying realism and time-locality, in terms of the amount of classical information needed to be transferred between successive measurements in order to simulate the above-mentioned correlations in successive measurements.
What compels quantum measurement to violate the Bell inequalities? Suppose that regardless of measurement, one can assign to a spin-
21 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 $\ifmmode\pm\else\textpm\fi{}1$ 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 $\ifmmode\pm\else\textpm\fi{}1$, 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-
21 particles and circuits for local quantum spin measurement can be used to win the game.
In quantum mechanics, joint measurements of noncommuting observables are only possible if a minimal unavoidable measurement uncertainty is accepted. On the other hand, correlations between noncommuting observables can exceed classical limits, as demonstrated by the violation of Bell's inequalities. Here, the relation between the uncertainty-limited statistics of joint measurements and the limits on expectation values of possible input states is analyzed. It is shown that the experimentally observable statistics of joint measurements explain the uncertainty limits of local states, but result in less restrictive bounds when applied to identify the limits of nonlocal correlations between two separate quantum systems. A tight upper bound is obtained for the four correlations that appear in the violation of Bell's inequalities and the statistics of pure states saturating the bound is characterized. The results indicate that the limitations of quantum nonlocality are a necessary consequence of the local features of joint measurements, suggesting the possibility that quantum nonlocality could be explained in terms of the local characteristics of quantum statistics.
Abstract Bell experiments measure correlations between outcomes of a number of observers measuring on a shared physical state emitted from a single source. Quantum correlations arising in such Bell experiments have been intensively studied over the last decades. Much less is known about the nature of quantum correlations arising in network structures beyond Bell experiments. Such networks can involve many independent sources emitting states to observers in accordance with the network configuration. Here, we will study classical and quantum correlations in a family of networks which can be regarded as compositions of several independent multipartite Bell experiments connected together through a central node. For such networks we present tight Bell-type inequalities which are satisfied by all classical correlations. We study properties of the violations of our inequalities by probability distributions arising in quantum theory.
It is generally believed that Bell's inequality holds for the case of entangled states, including two correlated particles or special states of a single particle. Here, we derive a single-particle Bell's inequality for two correlated spin states at two successive times, appealing to the statistical independence condition in an ideal experiment, for a locally causal hidden variables theory. We show that regardless of the locality assumption, the inequality can be violated by some quantum predictions.