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.
Highlights
The resource theory of quantum coherence is a vivid research topic, and various approaches in this direction have been presented over the past few years [1,2,3,4,5,6]
The corresponding class is called local incoherent operations and classical communication (LICC). We generalize these notions to separable operations known from entanglement theory [41,51,52], introducing separable incoherent (SI) operations, and separable quantum-incoherent (SQI) operations
We focus on the following four classes of operations: local incoherent operations and classical communication (LICC), local quantum-incoherent operations and classical communication (LQICC), separable incoherent operations (SI), and separable quantum-incoherent operations (SQI). We show that these classes obey inclusion relations very similar to those between local operations and classical communication (LOCC) and separable operations known from entanglement theory
Summary
The resource theory of quantum coherence is a vivid research topic, and various approaches in this direction have been presented over the past few years [1,2,3,4,5,6]. A quantum operation can be written in the form ΛðρÞ i1⁄4s cPallleKdliρnKco†l h, ewreitnht incoherent Kraus operators Kl, i.e., Kljmi ∼ jni, where jmi and jni are elements of the incoherent basis Significant progress within this resource theory has been achieved by Winter and Yang [39]. Chitambar and Gour [42] introduced the concept of physical incoherent operations These operations have a free dilation if one allows incoherent projective measurements on the ancilla followed by classical processing of the outcomes. As has been shown in several recent works, quantum coherence plays an important role in various tasks that are based on the laws of quantum mechanics One such task is quantum state merging, which was first introduced and studied in Reffs. VI, we expect that the ideas we present in this work will find applications beyond quantum information theory, most prominently in quantum thermodynamics and related research areas
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