Operational approach to entanglement and how to certify it

Abstract

Entangled physical systems are an important resource in quantum information. Some authors claim that in fact all quantum states are entangled. In this paper we show that this claim is incorrect and we discuss in operational way differences existing between separable and entangled states. A sufficient condition for entanglement is the violation of Bell-CHSH-CH inequalities and/or steering inequalities. Since there exist experiments outside the domain of quantum physics violating these inequalities therefore in the operational approach one cannot say that the entanglement is an exclusive quantum phenomenon. We also explain that an unambiguous experimental certification of the entanglement is a difficult task because classical statistical significance tests may not be trusted if sample homogeneity cannot be tested or is not tested carefully enough.

Entanglement between total intensity and polarization for pairs of coherent states

“…Thus entanglement in pairs of Glauber coherent states is consistent with previous evidences of nonclassical behavior as revealed by negativity of numberphase Wigner functions [4], nonclassical statistics in photon number detection [5], and unbalanced double homodyne detection [6], as well as other results [7]. This also fits with the idea that entanglement may be a more widespread property than naively expected [8][9][10].…”

Is the Moon There If Nobody Looks: Bell Inequalities and Physical Reality

“…In SPCE, "photon pairs, " prepared by a source, are described by a density matrix ρ and physical observables A and B by Hermitian operators 1 = ⊗ I andB 1 = I ⊗B defined on a Hilbert space H = H 1 ⊗ H 2 . The correlations between measured values of these observables are evaluated using a conditional covariance between A and B [56,58]:…”

Bell Inequalities, Experimental Protocols and Contextuality

“…In QT signals prepared by a source in SPCE are described by density matrices ρ and physical observables measured (random variables A and B describing the outcomes on the distant detectors) by hermitian operators and . The correlations between outcomes observed by Alice and Bob for each fixed setting of PBS are found using conditional covariance between A and B [37,38]:…”