Review of entangled coherent states

Abstract

We review entangled coherent state research since its first implicit use in 1967 to the present. Entangled coherent states are important to quantum superselection principles, quantum information processing, quantum optics, and mathematical physics. Despite their inherent fragility they have produced in a conditional propagating-wave quantum optics realization. Fundamentally the states are intriguing because they are entanglements of the coherent states, which are in a sense the most classical of all states of a dynamical system. Contents

Tomography onf-oscillators

“…The Schrödinger cat states defined as an even and odd superpositions of coherent states with opposite phases are introduced in [24] (see also review articles [66,67]). There exist lots of proposal for generating these states (see for example [68,69]).…”

Entanglement of Multi-qudit States Constructed by Linearly Independent Coherent States: Balanced Case

“…To this aim we first need to have the superposition of even and odd number of coherent states like as |α + µ|β and |α + µ 1 |β + µ 2 |γ , (up to normalization factors), and so on. In general, the superpositions of coherent states are difficult to produce, and fundamentally this could be due to extreme sensitivity to environmental decoherence (see, e.g., [14,15,29,30,31,32,33]). Here we restrict ourselves to the even cases.…”

Generating non-classical states from spin coherent states via interaction with ancillary spins

“…In the optical regime it is well known that such an interaction can create interesting path-entangled states for suitable non-classical input states. An example is entangled coherent states (ECSs) [7,32,33], which have been demonstrated to be a useful resource for quantum enhanced metrology [8,9]. These are created by the mixing of a Schrödinger cat-type state and a coherent state on a BS and by analogy to the optical case, similar states may be created in spin systems.…”

“…Recently, continuous-variable (CV) superposed/entangled states have shown their potential in various optical and photonic experiments [6] and the use of CV entangled states can be robust in practical quantum metrology [7,8,9].…”