Entanglement: quantum or classical?

Abstract

From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedanken experiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.

In Praise of Quantum Uncertainty

“…In what follows, we will begin with simple, yet deep, manifestations of quantum uncertainty, and then we shall discuss more recent ones, including a few novel implications of uncertainty for various quantum phenomena, and mainly nonlocality [ 13 , 14 , 15 , 16 ]. The latter results may be found in Section 4 .…”

The Riccati Equation and the Hidden Parameter &Variable

“…The hidden variable in quantum theory has been argued for a long time [7]. One of the difficulties in evaluating these contradictory results is that no exact mathematical criterion is given to enable one to judge the degree of success of these proposals.…”

Single‐Particle Entanglement

“…We refer the interested reader to the many papers dealing with this subject (see e.g., refs. [88,[91][92][93]).…”

“…Only here, the well known problems with locality or non‐contextuality arise with the photons of the considered light beam. [ 92,93 ] As a matter of fact, a complete classical description of the Bell inequality in this classical context is presented in, [ 94 ] where the violation of the CHSH inequality is ascribed to particular coherence properties of the light beam. It is important to remark that in this case the S parameter is a figure of merit which describes collective properties of the light beam, instead of the particular form of the state vector of the single photons.…”