Entanglement - A Queer In The World Of Quantum : Some Perspectives

TL;DR

This paper explores the peculiar features of entangled quantum states, including their transformations, roots of incomparability, and introduces a new class of activable bound entangled states with unique properties.

Contribution

It provides new insights into bipartite state transformations, links incomparability to fundamental no-go theorems, and introduces a novel class of activable bound entangled states with distinctive features.

Findings

Incomparable states can be transformed locally using free entanglement.

Incomparability relates to no-flipping and anti-unitary principles.

A new class of activable bound entangled states with unique properties is identified.

Abstract

The work is intended to represent some interesting and apparently peculiar features of entangled system in both pure as well as mixed states level. In the pure state level, we are largely concerned about the existence and characteristics of bipartite incomparable pair of states. We have found some schemes for local transformation of one pure bipartite state to another, incomparable in nature, by exploiting free unpreserved entanglement. Also, we observed that different incomparable pair of states in $3\times 3$ may co-operate with each other to cross the barrier of incomparability. Our next goal was to probe critically the roots of the existence of incomparable states. We have succeeded in connecting incomparability with some famous no-go theorems of quantum mechanics. We have established it with no-flipping principle, general anti-unitary operators and lastly with inner product preserving operations. Thus we are able to pose incomparability as a good detector of some non-physical operations. In the next part, we provide a new class of multipartite bound entanglement in mixed state level. The class of states are activable bound entangled. There are exactly four orthogonal activable bound entangled states in any even number of qubit system. They have some interesting features like Bell correlation, permutation symmetry, local Pauli connection, non-compatibility, etc. Apart from those properties, the class of bound entangled states have the remarkable feature of local indistinguishability in quantum systems.