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 to consider a reduced setting as well, namely the one with only the wire connected to a single quantum system, which leads to discord-like 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.
Highlights
One of the oldest questions in the field of quantum mechanics is how quantum states differ from classical states
In the resource theory that we introduce, local operations and physical wires (LOP), the wire is explicitly included in the description
One can, in all three possible two-wire settingps ffiffiLOPðQp1ffi⇜→ffi W1←⇝Q21. On this site (Q2)⇜→W2←⇝Q3), prepare jW3i from 1= 6ðj0iþ 2j1iÞW1 ⊗ðj0iþj1iÞW2, while the bipartite entanglement one can produce on the bipartition Q1, ðQ2 ⊗ Q3Þ is not enough to prepare jGHZ3i: As on any bipartition, one needs to prepare a fully entangled qubit, and this is equivalent to a maximally coherent qubit; the state with minimal coherence to prepare jGHZ3i is given by 1=2ðj0i þ j1iÞW1 ⊗ ðj0i þpffijffi1iÞW2, pwhffiffiich is strictly more coherent on W1 than 1= 6ðj0iþ
Summary
One of the oldest questions in the field of quantum mechanics is how quantum states differ from classical states. Some advances in understanding the resources in DQC1 have recently been made using a different form of nonclassicality, called coherence, which is exhibited by superpositions of states in a fixed orthonormal basis, whose elements and their statistical mixtures are the incoherent states [22,23,24,25] Based on this theory, complementing recently studied connections between entanglement and coherence [26,27,28,29,30,31,32,33,34,35,36,37,38,39], it was shown that the precision of the DQC1 protocol is a function of the coherence of the qubit one uses as a control and that any state with some property called basis-dependent discord [39,40,41,42,43] is a resource in this setting [42,43]. It is this “universal character” [47] of entanglement that motivates the present paper
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