Collectibility for Mixed Quantum States

TL;DR

This paper extends the concept of collectibility, used for pure states, to mixed quantum states, providing new bounds and tests for entanglement detection in multipartite systems using collective measurements.

Contribution

It introduces collectibility for mixed states and derives bounds for entanglement detection, enhancing previous pure state methods.

Findings

Derived bounds for collectibility of mixed states

Provided a new entanglement test for pseudopure two-qubit states

Linked collectibility bounds to the structure of entangled states

Abstract

Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for pure states only [Phys. Rev. Lett. 107, 150502 (2011)], is extended here for mixed quantum states. We define collectibility for any mixed states of a multipartite system. Deriving bounds for collectibility for positive partially transposed states of given purity provides a new insight into the structure of entangled quantum states. In case of two qubits the application of complementary measurements and coincidence based detections leads to a new test of entanglement of pseudopure states.