Abstract
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.
- Received 20 February 2018
- Revised 25 April 2018
DOI:https://doi.org/10.1103/PhysRevX.8.031005
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
One of the oldest questions in quantum mechanics is how quantum states differ from everyday, classical states. While the answer “it depends” is correct, researchers would like to more rigorously understand and quantify this difference. This would help in a number of areas, from understanding the impact of quantum mechanics on biological systems to objective comparisons of different quantum computing platforms. Here, we take a step toward truly understanding what it means for a system to be quantum by unifying different perspectives on the quantum-classical divide.
A clear manifestation of nonclassicality is entanglement. This property can be generated by two spatially separated experimenters, Alice and Bob, if they can send quantum particles to each other but not if they can only communicate classically (e.g., through a phone). Thus, there is no transparent way to make a classical (i.e., stochastic) model for its behavior—entanglement is therefore nonclassical.
However, many systems are neither entangled nor classical. For this reason, more general approaches have been considered to qualify a system as nonclassical. Our theory unifies many of these approaches by modeling the communication between Alice and Bob to be explicitly carried by a physical system, a “wire.” Entanglement between Alice and Bob is then quantified as usual, but the theory is more general, as it allows one to consider the perspective of the wire connecting the two. This theory yields a transparent way to model the wire as exactly classical if it cannot be used to generate entanglement.
Our theory unifies different known nonclassical features and allows us to quantify and compare them. This is important if one wants to understand and meaningfully discuss the value of nonclassicality.