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arXiv:1009.2571 · Physical Review A

Entanglement, discord, and the power of quantum computation

Aharon Brodutch, Daniel R. Terno

Published Jan 7, 2011• 80 citations
arXivHTMLPDF

Abstract

We show that the ability to create entanglement is necessary for execution of bipartite quantum gates even when they are applied to unentangled states and create no entanglement. Starting with a simple example we demonstrate that to execute such a gate bilocally the local operations and classical communications (LOCC) should be supplemented by shared entanglement. Our results point to the changes in quantum discord, which is a measure of quantumness of correlations even in the absence of entanglement, as the indicator of failure of a LOCC implementation of the gates.

DOI
10.1103/physreva.83.010301

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We show that the ability to create entanglement is necessary for execution of bipartite quantum gates even when they are applied to unentangled states and create no entanglement. Starting with a simple example we demonstrate that to execute such a gate bilocally the local operations and classical communications (LOCC) should be supplemented by shared entanglement. Our results point to the changes in quantum discord, which is a measure of quantumness of correlations even in the absence of entanglement, as the indicator of failure of a LOCC implementation of the gates.
Quantum discord is a measure of the quantumness of correlations. After reviewing its different versions and properties, we apply it to the questions of quantum information processing. First we show that changes in discord in the processed unentangled states indicate the need for entanglement in the distributed implementation of quantum gates. On the other hand, it was shown that zero system-environment discord is a necessary and sufficient condition for applicability of the standard completely positive description of the system's evolution. We demonstrate that this result does not translate into useful quantum process tomography. Depending on the details of the preparation procedure only absence of any initial correlations may guarantees consistency of the process tomography.
Quantum discord is a measure of the quantumness of correlations. After reviewing its different versions and properties, we apply it to the questions of quantum information processing. First we show that changes in discord in the processed unentangled states indicate the need for entanglement in the distributed implementation of quantum gates. On the other hand, it was shown that zero system-environment discord is a necessary and sufficient condition for applicability of the standard completely positive description of the system's evolution. We demonstrate that this result does not translate into useful quantum process tomography. Depending on the details of the preparation procedure only absence of any initial correlations may guarantees consistency of the process tomography.
Discordant states appear in a large number of quantum phenomena and seem to be a good indicator of divergence from classicality. While there is evidence that they are essential for a quantum algorithm to have an advantage over a classical one, their precise role is unclear. We examine the role of discord in quantum algorithms using the paradigmatic framework of restricted distributed quantum gates and show that manipulating discordant states using local operations has an associated cost in terms of entanglement and communication resources. Changing discord reduces the total correlations and reversible operations on discordant states usually require nonlocal resources. Discord alone is, however, not enough to determine the need for entanglement. A more general type of similar quantities, which we call KKK discord, is introduced as a further constraint on the kinds of operations that can be performed without entanglement resources.
Quantum discord characterizes "nonclassicality" of correlations in quantum mechanics. It has been proposed as the key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. We obtain a necessary and sufficient condition for the existence of nonzero quantum discord for any dimensional bipartite states. This condition is easily experimentally implementable. Based on this, we propose a geometrical way of quantifying quantum discord. For two qubits this results in a closed form of expression for discord. We apply our results to the model of deterministic quantum computation with one qubit, showing that quantum discord is unlikely to be the reason behind its speedup.
In this work (multipartite) entanglement, discord, and coherence are unified as different aspects of a single underlying resource theory defined through simple and operationally meaningful elemental operations. This is achieved by revisiting the resource theory defining entanglement, local operations, and classical communication (LOCC), placing the focus on the underlying quantum nature of the communication channels. Taking the natural elemental operations in the resulting generalization of LOCC yields a resource theory that singles out coherence in the wire connecting the spatially separated systems as an operationally useful resource. The approach naturally allows us to consider a reduced setting as well, namely, the one with only the wire connected to a single quantum system, which leads to discordlike resources. The general form of free operations in this latter setting is derived and presented as a closed form. We discuss in what sense the present approach defines a resource theory of quantum discord and in which situations such an interpretation is sound—and why in general discord is not a resource. This unified and operationally meaningful approach makes transparent many features of entanglement that in LOCC might seem surprising, such as the possibility to use a particle to entangle two parties, without it ever being entangled with either of them, or that there exist different forms of multipartite entanglement.
Quantum correlations between parts of a composite system most clearly reveal themselves through entanglement. Designing, maintaining, and controlling entangled systems is very demanding, which raises the stakes for understanding the efficacy of entanglement-free, yet quantum correlations, exemplified by quantum discord. Discord is defined via conditional mutual entropies of parts of a composite system and its direct measurement is hardly possible even via full tomographic characterization of the system state. Here we design a simple protocol to detect and quantify quantum discord in an unentangled bipartite system. Our protocol relies on a characteristic of discord that can be extracted from repeated direct measurements of certain correlations between subsystems of the bipartite system. The proposed protocol opens a way of extending experimental studies of discord to electronic systems, but can also be implemented in quantum-optical systems.