A new quantum correlation in terms of the average distance between the reduced state and the i-th output reduced states under local von Neumann measurements is proposed. It is shown that only the product states do not contain this quantum correlation and thus it is different from both the quantum discord (QD) Ollivier and Zurek (Phys. Rev. Lett. 88, 017901 (2001)) and the measurement-induced nonlocality (MIN) Luo and Fu (Phys. Rev. Lett. 106, 120401 (2011)). For pure states, it is twice of the quantity MIN, and is smaller than QD and entanglement of formation (EOF). A general analytical formula is given and a lower bound for the two qubits case is obtained. Furthermore, we compare it with EOF and QD through the Werner state and the isotropic state respectively.
Quantum correlation von Neuman measurement Averaged distance Reduced state
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We thank all referees for their helpful comments. Y. Guo is supported by the Natural Science Foundation of China (Grant No. 11301312, Grant No. 11171249) and the Natural Science Foundation of Shanxi (Grant No. 2013021001-1, Grant No. 2012011001-2). B. Li is supported by the Natural Science Foundation of China (Grant No. 11305015), the Natural Science Foundation of Jiangxi Province (Grant No. 20132BAB212010). H. Fan is supported by the ‘973’ program (Grant No. 2010CB922904). This paper is dedicated to professor Jinchuan Hou for his sixtieth birthday.