Quantum correlation cost of the weak measurement

TL;DR

This paper introduces the quantum correlation cost (QCC) based on trace norm, linking it to quantum discord and showing how residual quantumness can be extracted through weak or von Neumann measurements, demonstrated on Bell-diagonal states.

Contribution

It defines the quantum correlation cost (QCC) based on trace norm and explores its relation to quantum discord and residual quantumness extraction methods.

Findings

QCC is proportional to trace-norm quantum discord (TQD) with a factor depending on measurement strength.

Residual quantumness can be extracted via further weak measurements or sequences of infinitesimal weak measurements.

Demonstrated results using Bell-diagonal states.

Abstract

Quantum correlation cost (QCC) characterizing how much quantum correlation is used in a weak-measurement process is presented based on the trace norm. It is shown that the QCC is related to the trace-norm-based quantum discord (TQD) by only a factor that is determined by the strength of the weak measurement, so it only catches partial quantumness of a quantum system compared with the TQD. We also find that the residual quantumness can be `extracted' not only by the further von Neumann measurement, but also by a sequence of infinitesimal weak measurements. As an example, we demonstrate our outcomes by the Bell-diagonal state.