The entanglement or separability of mixed quantum states as a matter of the choice of observables

TL;DR

This paper explores how the classification of quantum states as entangled or separable depends on the choice of observables, revealing that such properties are not intrinsic but context-dependent, especially for mixed states.

Contribution

It systematically analyzes the dependence of entanglement on observable choices, highlighting differences between pure and mixed states and providing illustrative examples.

Findings

Pure states can always be made to appear entangled or separable by choosing observables.

For mixed states, the ability to represent states as entangled or separable depends on the factorization, but a general criterion is lacking.

Examples include quantum teleportation and the geometry of two-qubit states.

Abstract

In quantum systems, entanglement corresponds to nonclassical correlation of nonlocal observables. Thus, entanglement (or, to the contrary, separability) of a given quantum state is not uniquely determined by properties of the state, but may depend on the choice of the factorization of the algebra of observables. In the present work, we expose and systematize some recently reported results about the possibility to represent a single quantum state as either entangled or separable. We will distinguish in particular the cases of pure and mixed states. For pure states, it has been shown that observables can always be constructed such that any state has any amount of entanglement possible. For mixed states, the situation is more complex and only partial results are known: while it is always possible to choose a factorization such that a state appears separable, a general criterion to determine whether a state can be represented as entangled is not known. These results will be illustrated by several examples, the phenomenon of quantum teleportation, and the geometry of the states of two qubits.