Deep insight can be gained into the nature of nonclassical correlations by studying the quantum operations that create them. Motivated by this we propose a measure of nonclassicality of a quantum operation utilizing the relative entropy to quantify its commutativity with the completely dephasing operation. We show that our measure of nonclassicality is a sum of two independent contributions, the generating power -its ability to produce nonclassical states out of classical ones, and the distinguishing power -its usefulness to a classical observer for distinguishing between classical and nonclassical states. Each of these effects can be exploited individually in quantum protocols. We further show that our measure leads to an interpretation of quantum discord as the difference in superdense coding capacities between a quantum state and the best classical state when both are produced at a source that makes a classical error during transmission.Introduction. Identifying the resources that underlie quantum advantages in quantum communication and information processing is a crucial question of fundamental and technological importance. Generally, quantum entanglement is ascribed this role due to its necessity in a number of tasks exhibiting quantum advantages [1,2]. However, quantum enhancements are possible in certain computations with limited amounts of entanglement or even none at all when the involved quantum state is mixed [3][4][5][6][7]. Universal quantum computation with pure states also appears to be possible with little entanglement [8]. In addition to computational advantages, quantum communication can also exhibit advantages over classical communication in the absence of entanglement [9][10][11].Recently, it has been suggested that correlations beyond quantum entanglement might provide an explanation behind quantum enhancements. One of the most common quantities is the quantum discord [12][13][14][15]. Quantum discord has recently been interpreted as the difference in the performance of the quantum state merging protocol between a state and its locally decohered equivalent [16], and secondly as quantifying the amount of entanglement consumption in the quantum state merging protocol [17]. The role of quantum discord in a more general family of protocols has also been studied [18].An important difference between quantum discord and entanglement is that the latter is non-increasing, on average, under local operations and classical communication. This is the underlying principle of the resource theory of quantum entanglement. On the other hand, local operations can actually increase quantum discord [19][20][21][22]. Discordant states can be created out of classical states by a local channel if and only if the channel changes the local algebraic structure [23], and several authors have studied the evolution of quantum discord under various forms of dynamics [24][25][26][27][28]. However, the principles underlying the creation of nonclassical correlations from quantum operations are still lacking.Here we investiga...
The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of motion to predict the time evolution of quantum entanglement [Nature Physics, 4(4): 99, 2008]. Here we cast these recent results into a tensor network framework and in doing so, construct a theory which exposes the topological equivalence of the evolution of a family of entanglement monotones in arbitrary dimensions. This unification was accomplished by tailoring a form of channel state duality through the interpretation of graphical tensor network rewrite rules. The introduction of tensor network methods to the theory of entanglement evolution opens the door to apply methods from the rapidly evolving area known as tensor network states.
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