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arXiv:1610.02477 · Physical Review A

Remote creation of quantum coherence

Teng Ma, Ming‐Jing Zhao, Shao-Ming Fei, Gui‐Lu Long

Published Oct 7, 2016• 16 citations
arXivHTMLPDF

Abstract

We study remote creation of coherence (RCC) for a quantum system, A, with the help of quantum operations on another system, B, and one-way classical communication. We show that all the nonincoherent quantum states are useful for RCC and all the incoherent-quantum states are not. The necessary and sufficient conditions of RCC for the quantum operations on system B are presented for pure states. The upper bound of average RCC is derived, giving a relation among the entanglement (concurrence), the RCC of the given quantum state, and the RCC of the corresponding maximally entangled state. Moreover, for two-qubit systems we find a simple factorization law for the average remote-created coherence.

DOI
10.1103/physreva.94.042312

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We study remote creation of coherence (RCC) for a quantum system, A, with the help of quantum operations on another system, B, and one-way classical communication. We show that all the nonincoherent quantum states are useful for RCC and all the incoherent-quantum states are not. The necessary and sufficient conditions of RCC for the quantum operations on system B are presented for pure states. The upper bound of average RCC is derived, giving a relation among the entanglement (concurrence), the RCC of the given quantum state, and the RCC of the corresponding maximally entangled state. Moreover, for two-qubit systems we find a simple factorization law for the average remote-created coherence.
Abstract Quantum coherence and quantum correlation are two fundamental resources in quantum information and computation. Quantum correlated states in a bipartite system are the same as the states that are coherent with respect to any product basis, while a coherent state with respect to some given product basis may not be quantum correlated. In this work, we focus on the question of creating quantum correlation from a coherent state via incoherent quantum operations. We compare characterizations of incoherent operations (IOs), maximally incoherent operations, genuinely incoherent operations and coherence-breaking operations and then explicit interrelations among these operations. Moreover, we give the specific forms of states in two-qubit systems, called super-coherent ones, that can be mapped to quantum correlated ones via some genuinely incoherent operation. We find that there exist some coherent states that are not super-coherent. Furthermore, we prove that a state can be mapped to a quantum correlated state via an incoherent operation if and only if it is coherent. Lastly, we prove that any maximally entangled state can be mapped to an incoherent one via some one-side coherence-breaking operation.
We study the average quantum coherence over the pure state decompositions of a mixed quantum state. An upper bound of the average quantum coherence is provided, and sufficient conditions for the saturation of the upper bound are shown. These sufficient conditions always hold for two- and three-dimensional systems. This provides a tool to estimate the average coherence experimentally by measuring only the diagonal elements, which remarkably requires less measurements compared with state tomography. We then describe the pure state decompositions of the qubit state in the Bloch sphere geometrically. For any given qubit state, the optimal pure state decomposition achieving the maximal average quantum coherence as well as three other pure state decompositions are shown in the Bloch sphere. The order relations among their average quantum coherence are invariant for any coherence measure. The results presented in this paper are universal and suitable for all coherence measures.
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 apply these results to the task of assisted coherence distillation, where the aim is to locally extract maximally coherent states. For all pure states and certain mixed states we observe a collapse of all classes: the distillation rate is always the same. It remains open if the distillation rate can be different for general mixed states, and if the intersection of LOCC and SI is equivalent to LICC. We also introduce the task of incoherent teleportation and show that perfect incoherent teleportation of one qubit is possible with one singlet and two bits of classical communication. The approach presented here opens new ways to study the resource theory of coherence in distributed scenarios.
Lying at the heart of quantum mechanics, coherence has recently been studied as a key resource in quantum information theory. Quantum steering, a fundamental notion originally considered by Schödinger, has also recently received much attention. When Alice and Bob share a correlated quantum system, Alice can perform a local measurement to 'steer' Bob's reduced state. We introduce the maximal steered coherence as a measure describing the extent to which steering can remotely create coherence; more precisely, we find the maximal coherence of Bob's steered state in the eigenbasis of his original reduced state, where maximization is performed over all positive-operator valued measurements for Alice. We prove that maximal steered coherence vanishes for quantum-classical states whilst reaching a maximum for pure entangled states with full Schmidt rank. Although invariant under local unitary operations, maximal steered coherence may be increased when Bob performs a channel. For a two-qubit state we find that Bob's channel can increase maximal steered coherence if and only if it is neither unital nor semi-classical, which coincides with the condition for increasing discord. Our results show that the power of steering for coherence generation, though related to discord, is distinct from existing measures of quantum correlation.
Shared entanglement between spatially separated systems is an essential resource for quantum information processing including long-distance quantum cryptography and teleportation. While purification protocols for mixed distributed entangled quantum states exist, it is not clear how to optimally distribute entanglement to remote locations. Here, we describe a deterministic protocol for generating a maximally entangled state between remote locations that only uses local operations on qubits, and requires no classical communication between the separated parties. The procedure may provide protection from decoherence before the entanglement is "activated," and could be useful for quantum key distribution.