Classical pure states are coherent states

Paulina Marian, Tudor A Marian

Abstract This paper aims to stress the role of the Cahill–Glauber quasi-probability densities in defining, detecting, and quantifying the non-classicality of field states in quantum optics. The distance between a given pure state and the set of all pure classical states is called here a geometric degree of non-classicality. As such, we investigate non-classicality of a pure single-mode state of the radiation field by using the coherent states as a reference set of pure classical states. It turns out that any such distance is expressed in terms of the maximal value of the Husimi Q function. As an insightful application we consider the de-Gaussification process produced when preparing a quantum state by adding p photons to a pure Gaussian one. For a coherent-state input, we get an analytic degree of non-classicality which compares interestingly with the previously evaluated entanglement potential. Then we show that addition of a single photon to a squeezed vacuum state causes a considerable enhancement of non-classicality, especially at weak and moderate squeezing of the original state. By contrast, addition of further photons is less effective.

Alastair Brodlie

Constantin Brif, A. Mann, M. Revzen

We review classical properties of harmonic-oscillator coherent states. Then we discuss which of these classical properties are preserved under the group-theoretic generalization of coherent states. We prove that the generalized coherent states of quantum systems with Lie-group symmetries are the unique Bell states, i.e., the pure quantum states preserving the fundamental classical property of satisfying Bell’s inequality upon splitting.

Brian P. Anderson

Chang‐shui Yu, He‐Shan Song

Based on a proposed coherence measure, we show that the local coherence of a bipartite quantum pure state (coherence of its reduced density matrix) is exactly the same as the minimal average coherence with all potential pure-state realizations under consideration. In particular, it is shown that bipartite concurrence of pure states just captures the maximal difference between local coherence and the average coherence of one subsystem induced by local operations on the other subsystem with the assistance of classical communications, which provides an alternative operational meaning for bipartite concurrence of pure states. The relation between concurrence and the proposed coherence measure can also be extended to bipartite mixed states.

S. Twareque Ali, Jean-Pierre Antoine, Jean‐Pierre Gazeau