Violation Of Bell-like Inequality Research Articles

Grothendieck bound in a single quantum system

Grothendieck’s bound is used in the context of a single quantum system, in contrast to previous work which used it for multipartite entangled systems and the violation of Bell-like inequalities. Roughly speaking the Grothendieck theorem considers a ‘classical’ quadratic form that uses complex numbers in the unit disc, and takes values less than 1. It then proves that if the complex numbers are replaced with vectors in the unit ball of the Hilbert space, then the ‘quantum’ quadratic form might take values greater than 1, up to the complex Grothendieck constant . The Grothendieck theorem is reformulated here in terms of arbitrary matrices (which are multiplied with appropriate normalisation prefactors), so that it is directly applicable to quantum quantities. The emphasis in the paper is in the ‘Grothendieck region’ , which is a classically forbidden region in the sense that cannot take values in it. Necessary (but not sufficient) conditions for taking values in the Grothendieck region are given. Two examples that involve physical quantities in systems with six and 12-dimensional Hilbert space, are shown to lead to in the Grothendieck region . They involve projectors of the overlaps of novel generalised coherent states that resolve the identity and have a discrete isotropy.

Entanglement-like properties in spin–orbit coupled ultra cold atom and violation of Bell-like inequality

We show that the general quantum state of synthetically spin–orbit coupled ultra cold bosonic atoms, whose condensate was experimentally created recently by Lin et al (2011 Nature 471, 83), shows entanglement between motional degrees of freedom (momentum) and internal degrees of freedom (hyperfine spin). We demonstrate the violation of Bell-like inequality (CHSH) for such states that provide a unique opportunity to verify fundamental principles like quantum contextuality for commutating observables which are not spatially separated. We analyze in detail the Rabi oscillation executed by such an atom-laser system and how this influences quantities like entanglement entropy, the violation of Bell-like inequality, etc. We also discuss the implications of our result in testing quantum contextuality and Bell’s Inequality violation by macroscopic quantum object like Bose–Einstein condensate of ultra cold atoms.

Violation of Bell inequalities in larger Hilbert spaces: robustness and challenges

We explore the challenges posed by the violation of Bell-like inequalities by d-dimensional systems exposed to imperfect state-preparation and measurement settings. We address, in particular, the limit of high-dimensional systems, naturally arising when exploring the quantum-to-classical transition. We show that, although suitable Bell inequalities can be violated, in principle, for any dimension of given subsystems, it is in practice increasingly challenging to detect such violations, even if the system is prepared in a maximally entangled state. We characterize the effects of random perturbations on the state or on the measurement settings, also quantifying the efforts needed to certify the possible violations in case of complete ignorance on the system state at hand.

Entanglement discrimination in multi-rail electron–hole currents

We propose a quantum-Hall interferometer that integrates an electron–hole entangler with an analyzer working as an entanglement witness by implementing a multi-rail encoding. The witness has the ability to discriminate (and quantify) spatial-mode and occupancy entanglement. This represents a feasible alternative to limited approaches based on the violation of Bell-like inequalities.

Statistical Gauge Theory for Relativistic Finite Density Problems**The project supported by National Natural Science Foundation of China under Grant No. 19875009

A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is shown that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems, namely, i) the statistical gauge invariance; ii) the dark components of the local observables; and iii) the fermion statistical blocking effects, based upon an asymptotic nonthermal ensemble. An application to models is presented to show the importance of the discussions.