Quantifying the Nonclassicality of Operations

Abstract

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...

Informational correlation between two parties of a quantum system: spin-1/2 chains

“…In this regard, one has to mention Ref. [27] where the quantumness of operations has been studied without the direct relation to the entanglement and discord, similar to our case.…”

“…Next, we calculate the matrix T using Eqs. (16,17,24,27). The explicit form of this matrix is very complicated, and it is not represented in this paper.…”

Coherence manipulation with dephasing-covariant operations

“…The crucial difference between MIO and DIO is that DIO neither create nor detect coherence, in the sense that measurement statistics under any incoherent measurement after a DIO operation Λ are the same regardless of whether the input state possessed any coherence or not: we have i|Λ(ρ)|i i|Λ(∆(ρ))|i for all i. These operations have previously been considered in various contexts [15,28], and indeed they admit several interpretations. The operations DIO can be regarded as inherently classical [23,28], as any classical (incoherent) observer is unable to distinguish Λ(ρ) from Λ • ∆(ρ), and hence is unable to say whether the coherence of ρ has been employed in the process.…”

Complete condition for nonzero quantum correlation in continuous variable systems

“…Interestingly, quantum correlation has found numerous applications [3] in addition to its initial motivation in pointer states [2]. For examples, relating to the difference between quantum and classical Maxwell's demons [4], its role in open dynamics [5], the local broadcasting of the quantum correlations [6,7], the phase transitions [8], its operational meaning in state merging protocols [9,10], activating multipartite entanglement [11], creating entanglement in the measurement process [12], to be a resource in quantum state discrimination [13], entanglement distribution [14,15], remote state preparation [16], observing the operational significance of quantum correlation consumption [17], guaranteeing a minimum precision in the optimal phase estimation protocol [18], interpretation as the difference in superdense coding capacities [19], and demonstrating that quantum discord cannot be shared [20].…”