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We point out that, if one accepts the validity of quantum mechanics, the Bell parameter for the polarization state of two photons can be measured in a simpler way than by the standard procedure [Clauser, Horne, Shimony, and Holt, Phys. Rev. Lett. 23, 880 (1969)]. The proposed method requires only two measurements with parallel linear-polarizer settings for Alice and Bob at 0 and 45 degrees, and yields a significantly smaller statistical error for a large Bell parameter.
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The experimental realization of successive non-demolition measurements on single microscopic systems brings up the question of ergodicity in Quantum Mechanics (QM). We investigate whether time averages over one realization of a single system are related to QM averages over an ensemble of similarly prepared systems. We adopt a generalization of von Neumann model of measurement, coupling the system to $N$ probes --with a strength that is at our disposal-- and detecting the latter. The model parallels the procedure followed in experiments on Quantum Electrodynamic cavities. The modification of the probability of the observable eigenvalues due to the coupling to the probes can be computed analytically and the results compare qualitatively well with those obtained numerically by the experimental groups. We find that the problem is not ergodic, except in the case of an eigenstate of the observable being studied.
We describe how to obtain information on a quantum-mechanical system by coupling it to a probe and detecting some property of the latter, using a model introduced by von Neumann, which describes the interaction of the system proper with the probe in a dynamical way. We first discuss single measurements, where the system proper is coupled to one probe with arbitrary coupling strength. The goal is to obtain information on the system detecting the probe position. We find the reduced density operator of the system, and show how Luders rule emerges as the limiting case of strong coupling. The von Neumann model is then generalized to two probes that interact successively with the system proper. Now we find information on the system by detecting the position-position and momentum-position correlations of the two probes. The so-called Wigners formula emerges in the strong-coupling limit, while Kirkwoods quasi-probability distribution is found as the weak-coupling limit of the above formalism. We show that successive measurements can be used to develop a state-reconstruction scheme. Finally, we find a generalized transform of the state and the observables based on the notion of successive measurements.
We discuss the connection between the incompatibility of quantum measurements, as captured by the notion of joint measurability, and the violation of Bell inequalities. Specifically, we present explicitly a given a set of non jointly measurable POVMs $mathcal{M}_A$ with the following property. Considering a bipartite Bell test where Alice uses $mathcal{M}_A$, then for any possible shared entangled state $rho$ and any set of (possibly infinitely many) POVMs $mathcal{N}_B$ performed by Bob, the resulting statistics admits a local model, and can thus never violate any Bell inequality. This shows that quantum measurement incompatibility does not imply Bell nonlocality in general.
Network Bell experiments give rise to a form of quantum nonlocality that conceptually goes beyond Bells theorem. We investigate here the simplest network, known as the bilocality scenario. We depart from the typical use of the Bell State Measurement in the network central node and instead introduce a family of symmetric iso-entangled measurement bases that generalise the so-called Elegant Joint Measurement. This leads us to report noise-tolerant quantum correlations that elude bilocal variable models. Inspired by these quantum correlations, we introduce network Bell inequalities for the bilocality scenario and show that they admit noise-tolerant quantum violations. In contrast to many previous studies of network Bell inequalities, neither our inequalities nor their quantum violations are based on standard Bell inequalities and standard quantum nonlocality. Moreover, we pave the way for an experimental realisation by presenting a simple two-qubit quantum circuit for the implementation of the Elegant Joint Measurement and our generalisation.
The analysis of the model quantum clocks proposed by Aharonov et al. [Phys. Rev. A 57 (1998) 4130 - quant-ph/9709031] requires considering evanescent components, previously ignored. We also clarify the meaning of the operational time of arrival distribution which had been investigated.
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