On Global Effects Caused by Locally Noneffective Unitary Operations

TL;DR

This paper explores how locally cyclic unitaries can detect entanglement in bipartite quantum states by measuring the global state changes, revealing connections to non-locality and CHSH inequality, with explicit formulas for key state classes.

Contribution

It introduces a novel entanglement detection criterion based on local cyclic unitaries and derives explicit formulas for its maximal effect on various quantum states.

Findings

The criterion detects entanglement in pure, Werner, and two-qubit states.

It exhibits behavior similar to non-locality anomalies in higher dimensions.

For certain two-qubit states, it is equivalent to the CHSH inequality.

Abstract

Given a bipartite quantum state rho with subsystems A and B of arbitrary dimensions, we study the entanglement detecting capabilities of locally noneffective, or cyclic, unitary operations [L. B. Fu, Europhys. Lett., vol. 75, pp. 1-7, 2006]. Local cyclic unitaries have the special property that they leave their target subsystem invariant. We investigate the distance between rho and the global state after local application of such unitaries as a possible indicator of entanglement. To this end, we derive and discuss closed formulae for the maximal such distance achievable for three cases of interest: (pseudo)pure quantum states, Werner states, and two-qubit states. What makes this criterion interesting, as we show here, is that it surprisingly displays behavior similar to recent anomalies observed for non-locality measures in higher dimensions, as well as demonstrates an equivalence to the CHSH inequality for certain classes of two-qubit states. Yet, despite these similarities, the criterion is not itself a non-locality measure. We also consider entanglement detection in bound entangled states.