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Bell test with time-delayed two-particle correlations

A. V. Lebedev, G. Blatter

Published Jun 23, 2007• 0 citations
OpenAlex

Abstract

Adopting the frame of mesoscopic physics, we describe a Bell type experiment involving time-delayed two-particle correlation measurements. The indistinguishability of quantum particles results in a specific interference between different trajectories. We show how the non-locality in the time-delayed correlations due to the indistinguishability of the quantum particles manifests itself in the violation of a Bell inequality, where the degree of violation is related to the accuracy of the measurement. We demonstrate how the interrelation between the orbital- and the spin exchange symmetry can by exploited to infer knowledge on spin-entanglement from a measurement of orbital entanglement.

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Adopting the frame of mesoscopic physics, we describe a Bell type experiment involving time-delayed two-particle correlation measurements. The indistinguishability of quantum particles results in a specific interference between different trajectories. We show how the non-locality in the time-delayed correlations due to the indistinguishability of the quantum particles manifests itself in the violation of a Bell inequality, where the degree of violation is related to the accuracy of the measurement. We demonstrate how the interrelation between the orbital- and the spin exchange symmetry can by exploited to infer knowledge on spin-entanglement from a measurement of orbital entanglement.
Adopting the frame of mesoscopic physics, we describe a Bell-type experiment involving time-delayed two-particle correlation measurements. The indistinguishability of quantum particles results in a specific interference between different trajectories; the nonlocality in the time-delayed correlations manifests itself in the violation of a Bell inequality, with the degree of violation related to the accuracy of the measurement. In addition, we demonstrate how the interrelation between the orbital- and the spin-exchange symmetry can by exploited to infer knowledge on spin entanglement from a measurement of orbital entanglement.
We study the time-dependent electron-electron and electron-hole correlations in a mesoscopic device which is splitting an incident current of free fermions into two spatially separated particle streams. We analyze the appearance of entanglement as manifested in a Bell inequality test and discuss its origin in terms of local spin-singlet correlations already present in the initial channel and the action of post-selection during the Bell-type measurement. The time window over which the Bell inequality is violated is determined in the tunneling limit and for the general situation with arbitrary transparencies. We compare our results with alternative Bell inequality tests based on coincidence probabilities.
Entanglement between two separate systems is a necessary resource to violate a Bell inequality in a test of local realism. We demonstrate that to overcome the Bell bound, this correlation must be accompanied by the entanglement between the constituent particles. This happens whenever a super-selection rule prohibits coherences between states with different total number of particles and thus imposes a constraint on feasible local operations in each sub-system. We show that the necessary entanglement between the particles might solely result from their indistinguishability. We also give an example of both mode and particle-entangled pure state, which does not violate any Bell inequality. Our result reveals a fundamental relation between the non-locality and the particle entanglement.
Violation of local realism via Bell inequality-a profound and counterintuitive manifestation of quantum theory that conflicts with the prediction of local realism-is viewed to be intimately linked with quantum entanglement. Experimental demonstrations of such a phenomenon using quantum entangled states are among the landmark experiments of modern physics and paved the way for quantum technology. Here, we report the violation of the Bell inequality that cannot be described by quantum entanglement in the system but arises from quantum indistinguishability by path identity, shown by the multiphoton frustrated interference. By analyzing the measurement of four-photon frustrated interference within the standard Bell-test formalism, we find a violation of Bell inequality by more than four SDs. Our work establishes a connection between quantum correlation and quantum indistinguishability, providing insights into the fundamental origin of the counterintuitive characteristics observed in quantum physics.
Bell-type experiments that test correlated observables typically involve measurements of spin or polarization on multi-particle systems in singlet states. These observables are all non-commuting and satisfy an uncertainty relation. Theoretically, the non-commuting nature should be independent of whether the singlet state consists of multiple particles or a single particle. In addition, if Bell-type inequalities can be found for experiments involving spin and polarization, the same should be true for experiments involving other non-commuting observables such as position and momentum. In fact the original EPR paper used position and momentum, though in a different experimental situation. As such, an experiment is proposed to measure (quantum mechanically) position and momentum for a single oscillator as a means for deriving a Bell-type inequality for these correlated observables. The experiment, if realizable, would shed light on the basic nature of matter, perhaps pointing to some form of self-entanglement, and would also help to further elucidate a possible mechanism behind the Heisenberg uncertainty principle. Violation of these inequalities would, in fact, offer yet another confirmation of the principle.
We propose a spin-independent scheme to generate and detect two-particle entanglement in a mesoscopic normal-superconductor system. A superconductor, weakly coupled to the normal conductor, generates an orbitally entangled state by injecting pairs of electrons into different leads of the normal conductor. The entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current cross correlators. It is shown that the Bell inequality can be violated for arbitrary strong dephasing in the normal conductor.