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Chinese Physics B

Effect of weak measurement on quantum correlations

L. Jebli, M Amzioug, Salah Eddine Ennadifi, Nabil Habiballah, Mostafa Nassik

Published Jul 15, 2020• 7 citations
Publisher

Abstract

We investigate the local quantum uncertainty (LQU ) in weak measurement. An expression of weak LQU is explicitly determined. Also, we consider some cases of three special X states, Werner state, circulant two-qubit states, and Heisenberg model via LQU in normal and weak measurements. We find that the LQU in weak measurement is weaker than the case of strong measurement.

DOI
10.1088/1674-1056/aba5fa

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We investigate the local quantum uncertainty (LQU ) in weak measurement. An expression of weak LQU is explicitly determined. Also, we consider some cases of three special X states, Werner state, circulant two-qubit states, and Heisenberg model via LQU in normal and weak measurements. We find that the LQU in weak measurement is weaker than the case of strong measurement.
Abstract Recently, local quantum uncertainty (LQU) as a measure of quantum correlations has been proposed by Girolami et al . We here have investigated the LQU dynamics in a pair of qubits system subjected to either local or collective classical phase noises. The explicit analytical expressions of LQU for the two-qubit system of interest initially in a Werner state under these dephasing noises have been derived. We compare the dynamics of LQU with that of entanglement as measured with concurrence. Our results show that LQU always decays asymptotically while the entanglement displays sudden death phenomenon. Besides, there is no simple relation between the LQU and entanglement since LQU may be smaller or larger than entanglement. Finally, we try to protect LQU against the dephasing noise by means of filtering operation.
Local quantum uncertainty is defined as the minimum amount of uncertainty in measuring a local observable for a bipartite state. It provides a well-defined measure of pairwise quantum correlations in quantum systems and has operational significance in quantum metrology. In this work, we analytically derive the expression of local quantum uncertainty for two-qubit [Formula: see text] states which are of paramount importance in various fields of quantum information. As an illustration, we consider two-qubit states extracted from even and odd spin coherent states.
Abstract Many measures of quantum correlations have been introduced so far, and now their properties are carefully studied both theoretically and experimentally. The most important among them are quantum entanglement and quantum discord. Recently, it was shown that the Wigner–Yanase skew information and quantum Fisher information also can serve as measures of nonclassical correlations. These discordlike measures are called local quantum uncertainty (LQU) and interferometric power or local quantum Fisher information (LQFI), correspondingly. In this paper the behavior of LQU and LQFI is considered at thermal equilibrium of the two-qubit Heisenberg models in the absence and presence of an external magnetic field; these cases correspond to the Bell-diagonal and general X states, respectively.
Abstract In this article, we study quantum coherence of bipartite state from the perspective of weak measurement, which generalizes the notion of coherence relative to measurement. This is being illustrated by computing coherence for the well-known Bell diagonal and Werner states. Further, we have expanded the notion of coherence to encompass correlations, exploring its connections with other quantifications of nonlocality. We have determined that this coherence measure can be perceived as a generalized version of the Wigner-Yanese skew information measure and several other nonlocal measures. As a natural extension, we introduce uncertainty relations within the context of weak measurements. Additionally, we propose a novel form of variance by considering the weak value of an observable within a comprehensive framework.
Among many applications quantum weak measurements have been shown to be important in exploring fundamental physics issues, such as the experimental violation of the Heisenberg uncertainty relation and the Hardy paradox, and have also technological implications in quantum optics, quantum metrology and quantum communications, where the precision of the measurement is as important as the precision of quantum state preparation. The theory of weak measurement can be formulated using the pre-and post-selected quantum systems, as well as using the weak measurement operator formalism. In this work, we study the quantum discord (QD) of quasi-Werner mixed states based on bipartite entangled coherent states using the weak measurements operator, instead of the projective measurement operators. We then compare the quantum discord for both kinds of measurement operators, in terms of the entanglement quality, the latter being measured using the concept of concurrence. It’s found greater quantum correlations using the weak measurement operators.