Quantum steering of Bell-diagonal states with generalized measurements

TL;DR

This paper develops a local hidden state model for quantum steering in Bell-diagonal two-qubit states under generalized measurements, expanding understanding beyond projective measurements and enabling systematic analysis of steerability.

Contribution

It introduces a model for generalized measurements on Bell-diagonal states, extending previous results limited to projective measurements, and sets criteria for steerability with broader measurement types.

Findings

Model exists if $R_T \,\ge\, 6/5$ for generalized measurements

Steerability criteria depend on the correlation matrix $T$ and integral $N_T$

Framework enables systematic study of quantum steerability beyond symmetric states

Abstract

The phenomenon of quantum steering in bipartite quantum systems can be reduced to the question whether or not the first party can perform measurements such that the conditional states on the second party can be explained by a local hidden state model. Clearly, the answer to this depends on the measurements which the first party is able to perform. We introduce a local hidden state model explaining the conditional states for all generalized measurements on Bell-diagonal states of two qubits. More precisely, it is known for the restricted case of projective measurements and Bell-diagonal states characterised by the correlation matrix $T$ that a local hidden state model exists if and only if $R_T= 2 \pi N_T |\det (T)| \ge 1$, where $N_T$ is defined by an integral over the Bloch sphere. For generalized measurements described by positive operator valued measures we construct a model if $R_T \ge 6/5$. Our work paves the way for a systematic study of steerability of quantum states with generalized measurements beyond the highly-symmetric Werner states.