Quantum Advantage Of Quantum States In Two Systems

In the last decades, quantum information has developed to be an interdisciplinary science, which is based upon quantum mechanics and classical information theory. The appears of quantum information provides protocols and algorithms for information processing, which may surpass their classical counterparts. As the development of this field, quantum entanglement is shown to be an important resource for some quantum information tasks, such as quantum cryptography、superdense coding and teleportation and so on. However, it seems that the entanglement is not able to explain all quantum correlation in bipartite system since the absence of entanglement does not eliminate all signatures of quantum behavior. In2001, people proposed a new quantity for nonclassical correlation, i.e., quantum discord, which is the measure of the discrepancy between the total and classical correlation. Gradually quantum discord has become the important resources in quantum information processing. For example, quantum discord is shown to be the quantum advantage in the analytical solution of the mixed states and the deterministic quantum computation with one qubit(DQC1) but with negligible entanglement. In2012, it was found that the discord consumption may be considered as the quantum advantage for encoding information. This is a clear evidence that quantum discord can be considered as a resource for quantum information processing like the role of entanglement in teleportation.In this paper, it is defined that quantum advantage is upper bounded by the consumption of discord during the encoding information and is lower bounded by the difference of discord consumption and classical correlation [Nature.Phys.10.1038]. Thus, quantum discord consumed during encoding can quantify the advantage of the coherent interactions. On this basis, we consider the quantum advantage as the best quantum advantage for the maximal encoding. Quantum discord is quantum measurement dependent, we show that the quantum advantage of bipartite system with POVM or projection measurement, weak measurement.The result shows that the extra quantumness of correlation can be obtained by weak measurement. During encoding, quantum discord induced by weak measurement is larger. The analytical expressions for quantum advantage in bipartite system with weak measurement are obtained for the case of general pure entangled states and the Bell-diagonal states. This highlights the fundamental role of weak measurements in studying quantum correlations, and also provides a new application of weak measurement in quantum information processing.