Super-quantum correlation and geometry for Bell-diagonal states with weak measurements

TL;DR

This paper introduces the concept of super one-way deficit via weak measurements, compares it with standard measures, and explores its geometric and dynamic properties in Bell-diagonal states, revealing insights into quantum correlations.

Contribution

It generalizes one-way deficit using weak measurements, analyzes its behavior in Werner states, and provides geometric visualization of super-quantum discord for Bell-diagonal states.

Findings

Super one-way deficit is smaller than the standard one-way deficit.

Weak measurement does not always capture more quantum correlations.

Super-quantum correlation remains unchanged under phase-flipping decoherence.

Abstract

We propose "super one-way deficit" by weak measurement as the generalization of one-way deficit defined for standard projective measurement. The super one-way deficit for Werner state is obtained analytically. We find that super one-way deficit is smaller than the standard one-way deficit, which contrasts with a straightforward expectation based on the known fact that super-quantum discord by weak measurement is always larger than the quantum discord defined by projective measurement. On the other hand, by tuning the weak measurement continuously to the projective measurement, both super one-way deficit and super-quantum discord converge to the same value, which is either the one-way deficit or the quantum discord both quantifying quantum correlation. In this sense, weak measurement does not necessarily capture more quantumness of correlations. We also give the geometry of super- quantum discord of the Bell-diagonal states with explicit geometrical figures. As an application, the dynamic behavior of super- quantum correlation including super-quantum discord and super one-way deficit under decoherence is investigated. We find that the order relation of the super-quantum correlation and the quantum correlation keep unchanged under the phase flipping channel for the Bell-diagonal states and the Werner states.