Towards Resource Theory of Coherence in Distributed Scenarios

Abstract

The search for a simple description of fundamental physical processes is an important part of quantum theory. One example for such an abstraction can be found in the distance lab paradigm: if two separated parties are connected via a classical channel, it is notoriously difficult to characterize all possible operations these parties can perform. This class of operations is widely known as local operations and classical communication (LOCC). Surprisingly, the situation becomes comparably simple if the more general class of separable operations is considered, a finding which has been extensively used in quantum information theory for many years. Here, we propose a related approach for the resource theory of quantum coherence, where two distant parties can only perform measurements which do not create coherence and can communicate their outcomes via a classical channel. We call this class local incoherent operations and classical communication (LICC). While the characterization of this class is also difficult in general, we show that the larger class of separable incoherent operations (SI) has a simple mathematical form, yet still preserving the main features of LICC. We demonstrate the relevance of our approach by applying it to three different tasks: assisted coherence distillation, quantum teleportation, and single-shot quantum state merging. We expect that the results obtained in this work also transfer to other concepts of coherence which are discussed in recent literature. The approach presented here opens new ways to study the resource theory of coherence in distributed scenarios. arXiv:1509.07456v3 [quant-ph]

Structure of the Resource Theory of Quantum Coherence

“…Such multipartite scenarios have been previously studied in Refs. [38][39][40][41], and the results presented in this letter provide a strong framework for their further investigation. Another important question which is left open in this work is the relation of Gibbs-preserving strictly incoherent operations to thermal operations.…”

“…The same is true for separable quantum-incoherent operations [41], i.e., operations of the form (6) with incoherent operators B i , and separable incoherent operations where both A i and B i are incoherent [41]. For single-qubit IO and SIO the upper bound in Proposition 3 gives 17 operators.…”

“…While initially formulated for a single particle, the framework of coherence has recently been extended to distributed scenarios [38][39][40][41]. This extension has found several applications in remote quantum protocols, including the tasks of quantum state merging [42,43] and assisted coherence distillation [38,41], which has also been demonstrated experimentally very recently [44].…”

Quantum Coherence and Intrinsic Randomness

“…The gap between the two strategies is equal to the discord of the bipartite state shared by Alice and Eve. The result provides a new link between single system quantumness and quantum correlations even in separable states, which was inspired by previous studies on the trade‐off between local and global quantum properties . Following this line of thinking, other interesting scenarios where the interplay between coherence and correlations should be investigated is in the context of physical limits to privacy and to communication, for example, data hiding protocols .…”

Analytically Computable Symmetric Quantum Correlations

“…[26][27][28][29][30][31][32][33][34][35][36][37][38][39] The same is true for its counterpart quantity, [40][41][42] that is, the measurementinduced nonlocality (MIN) which characterizes the global disturbance in a composite state caused by a local nondisturbing measurement on one subsystem. In particular, with the development of the resource theory of quantum coherence, [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70] it was shown that the coherence of a system could be converted through incoherent operations into the SQD, instead of the asymmetric QD, of a composite system. [42][43][44][45][46][47][48][49] However, neither the QD nor the MIN of a bipartite system is symmetric in the sense that different results will be obtained (especially for some zero-discord states) if the two subsystems are swapped, which implies that the QD and MIN cannot completely quantify all of the quantum correlations present in a state.…”