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arXiv:1409.4017 · Annals of Physics

Quantum correlation cost of the weak measurement

Jun Zhang, Shao-xiong Wu, Chang-shui Yu

Published Sep 6, 2014• 3 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2014.08.020

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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.
The concept of ergotropy was previously introduced as the maximum extractable work from a quantum state. Its enhancement, which is induced by quantum correlation via projective measurement, was formulated as the daemonic ergotropy. In this work, we investigate the ergotropy in the presence of quantum correlation via weak measurement because of its elegant effects on the measured system. By considering a bipartite correlated quantum system consisting of main and ancillary systems, we demonstrate that the extractable work by the non-selective weak measurement on the ancilla is always equal to the situation captured by the strong measurement. However, the selective weak measurement interestingly reveals more work than the daemonic ergotropy and the ergotropy of the total system is greater than or equal to the daemonic ergotropy. Moreover, it is shown that for Bell diagonal states, at the cost of losing quantum correlation, the total extractable and thus non-local extractable works can be increased by using measurement. Also, we find that there is no direct relationship between quantum correlation and non-local extractable work for these cases.