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International Journal of Quantum Information

Quantum correlation based on weak measurements

Yangyang Wang, Jinchuan Hou, Xiaofei Qi

Published Aug 23, 2017• 6 citations
Publisher

Abstract

A quantum correlation [Formula: see text] based on weak measurements for bipartite systems is introduced. It is shown that the product states do not contain this quantum correlation. Also, the necessary and sufficient condition for any two-qubit state becoming a product state is obtained. The quantum correlation [Formula: see text] and other quantum correlation for two-qubit entangled pure state, Werner states and isotropic states are compared.

DOI
10.1142/s0219749917500411

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A quantum correlation [Formula: see text] based on weak measurements for bipartite systems is introduced. It is shown that the product states do not contain this quantum correlation. Also, the necessary and sufficient condition for any two-qubit state becoming a product state is obtained. The quantum correlation [Formula: see text] and other quantum correlation for two-qubit entangled pure state, Werner states and isotropic states are compared.
We search a simplest and minimal way to determine whether a given quantum system is entangled or separable. For this end, we propose binary correlation measurements in which restricted knowledge of only zero or nonzero correlations is available. We consider the concrete investigation on a pure state for two particles, each particle having two basis states (the [Formula: see text] system). We show that, even with this limited information from the binary correlation measurements, we can still reach the known minimum of three measurements for entanglement detection. We next consider the comparable problem applied to the mixed density matrix. The mixed quantum case appears to require more detailed information, which we illustrate by studying the concrete example of the Werner density matrix.
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.
Based on the Pauli spin operators we develop the notion of the spin-correlation matrix for the two-qubit system. If this matrix is non-zero, the measure of the correlation between the qubits is the average of the non-zero elements. Trivially, for zero matrix the bipartite is uncorrelated. This criterion turns out to be a necessary and sufficient condition for the full correlation, where it includes information on both entanglement and correlation other than entanglement. Moreover, we discuss to what extent this criterion can give information on the entanglement of the system. The criterion is generic in the sense that it can be applied to mixed and pure systems. Also, it can be easily extended to treat the correlation of multipartite systems. We compare the results obtained from this criterion to those from concurrence for various examples and we gain agreement regarding entanglement. We believe that this criterion may have a wide range of potential applications in quantum information theory.
Bell inequalities are an essential part of quantum information theory. Based on these fundamental inequalities, we propose a different indicator for nonclassicality in the Bell sense: average correlation. We derive a general expression for average correlation and calculate its value for pure states and Werner states. From there we show how two inequalities emerge which serve as necessary and sufficient conditions for nonclassicality. They are simple to evaluate and can even be used to classify all bipartite qubit states.
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.