Quantum mutual information and quantumness vectors for multiqubit systems
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Quantum mutual information and quantumness vectors for multiqubit systems Sk Sazim1
· Pankaj Agrawal1
Received: 14 November 2019 / Accepted: 3 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We introduce a new information theoretic measure of quantum correlations for multiparticle systems. We use a form of multivariate mutual information—the interaction information—and generalize it to multiparticle quantum systems. There are a number of different possible generalizations. We consider two of them. One of them is related to the notion of quantum discord and the other to the concept of quantum dissension. This new measure, called dissension vector, is a set of numbers—quantumness vector. This can be thought of as a fine-grained measure, as opposed to measures that quantify some average quantum properties of a system. These quantities quantify/characterize the correlations present in multiparticle states. We consider some multiqubit states and find that these quantities are responsive to different aspects of quantumness and correlations present in a state. We find that different dissension vectors can track the correlations (both classical and quantum) or quantumness only. As physical applications, we find that these vectors might be useful in several information processing tasks. We consider the role of dissension vectors—(a) in deciding the security of BB84 protocol against an eavesdropper and (b) in determining the possible role of correlations in the performance of Grover search algorithm. Specially, in the Grover search algorithm, we find that dissension vectors can detect the correlations and show the maximum correlations when one expects. Keywords Quantum correlations · Mutual information · Entanglement
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Sk Sazim [email protected] Pankaj Agrawal [email protected]
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Institute of Physics, Sainik School Post, Bhubaneswar, Orissa 751005, India 0123456789().: V,-vol
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S. Sazim, P. Agrawal
1 Introduction In the quantum information science, one of the challenges is to understand the nature of correlations present in a multiparticle system. Because of its complex nature, we still have little success in this respect [1,2]. Correlations, specially quantum correlations, have been very useful for a host of quantum information processing tasks, such as quantum computing [3–5], quantum cryptography [6], and quantum metrology [7]. The quantum correlations also lie at the heart of quantum mysteries and account for many counterintuitive features of the quantum world. Therefore, a understanding of the nature of quantum correlations is very important. The correlations in a system can be of classical and/or quantum nature. Usually, it is believed that quantum correlations are due to entanglement [2]. However, more recently, it has been suggested that the quantum correlations go beyond the simple idea of entanglement [1]. In particular, it has been argued that quantum discord [8,9] quantifies all types of quantum correlations including entanglement. Dis
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