Given two pairs of quantum states, a fundamental question in the resource theory of asymmetric distinguishability is whether there exists a quantum channel converting one pair to the other. In this work, we reframe this question in such a way that a catalyst can be used to help perform the transformation, with the only constraint on the catalyst being that its reduced state is returned unchanged, so that it can be used again to assist a future transformation. What we find here, for the special case in which the states in a given pair are commuting, and thus quasiclassical, is that this catalytic transformation can be performed if and only if the relative entropy of one pair of states is larger than that of the other pair. This result endows the relative entropy with a fundamental operational meaning that goes beyond its traditional interpretation in the setting of independent and identical resources. Our finding thus has an immediate application and interpretation in the resource theory of asymmetric distinguishability, and we expect it to find application in other domains.
Monogamy of quantum correlations provides a way to study restrictions on their sharability in multiparty systems. We find the critical exponent of these measures, above which randomly generated multiparty pure states satisfy the usual monogamy relation, and show that the critical power decreases with the increase in the number of parties. For three-qubit pure states, we detect that W-class states are more prone to being nonmonogamous as compared to the GHZ-class states. We also observe a different criticality in monogamy power up to which random pure states remain nonmonogamous. We prove that the "average monogamy" score asymptotically approaches its maximal value on increasing the number of parties. Analyzing the monogamy scores of random three-, four-, five-and six-qubit pure states, we also report that almost all random pure six-qubit states possess maximal monogamy score, which we confirm by evaluating statistical quantities like mean, variance and skewness of the distributions. In particular, with the variation of number of qubits, means of the distributions of monogamy scores for random pure states approach to unitywhich is the algebraic maximum -thereby conforming to the known results of random states having maximal multipartite entanglement in terms of geometric measures. I. INTRODUCIONQuantum entanglement [1], one of the most striking features in quantum mechanics, is the essential resource [2] for a plethora of quantum information protocols like quantum teleportation [3], quantum dense coding [4], entanglement-based quantum cryptography [5], one-way quantum computation [6] etc. These protocols revolutionize the existing communication and computation schemes based on laws of classical mechanics. Due to immense importance of entanglement, over the years, several detection methods like partial transposition [7] based on positive maps [8], entanglement witness, [9][10][11], and quantifiers such as distillable entanglement [12], entanglement of formation [13,14], logarithmic negativity [15,16] have been proposed. On the other hand, it has also been realized that quantum mechanical systems can exhibit nonclassical phenomena which cannot be explained by using the theory of entanglement, and hence a different resource theory has been developed where unlike separable states, "classically correlated" states in the computational basis are the free states [17]. These measures, independent of entanglement, belonging to a finegrained paradigm of quantum correlations (QC), have their origin in the concepts of information theory or geometry of states or thermodynamics. Examples of such measures include quantum discord [18], geometric quantum discord [19], quantum work deficit [20,21], and quantum deficit [22] (see review [17]).Beyond the bipartite domain, understanding of QC, even for pure states shared by multiple parties, is limited due to its complex structure. In this paper, we study the distribution of QC among the various parties of a random multipartite quantum state, with the help of the concept of "monogamy" [...
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