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Results in Physics

Reduce coherence loss in coherence-assisted transformation

Hai‐Bo Xing, Ming Yang

Published Apr 18, 2020• 4 citations
Publisher

Abstract

We discuss the coherence-assisted transformation of pure coherent states under incoherent operations and show that the amount of coherence loss can be reduced with the help of the auxiliary coherent state. Starting with the simplest case i.e., the main coherent state and auxiliary coherent state are both 2×2 dimensional, we compare the change of coherence before and after the transformation and find that the amount of coherence loss can be reduced due to the increase of the coherence of auxiliary coherent state. In general, when the main coherent state and auxiliary coherent state are high-dimensional, the result is also true. For the coherence of auxiliary coherent state is increased, we can get the maximally coherent state at some conditions, this case can be viewed as a new way for the distillation of coherent state. These interesting results of coherence transformation will give us a better understanding of the resource manipulation.

DOI
10.1016/j.rinp.2020.103111

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We discuss the coherence-assisted transformation of pure coherent states under incoherent operations and show that the amount of coherence loss can be reduced with the help of the auxiliary coherent state. Starting with the simplest case i.e., the main coherent state and auxiliary coherent state are both 2×2 dimensional, we compare the change of coherence before and after the transformation and find that the amount of coherence loss can be reduced due to the increase of the coherence of auxiliary coherent state. In general, when the main coherent state and auxiliary coherent state are high-dimensional, the result is also true. For the coherence of auxiliary coherent state is increased, we can get the maximally coherent state at some conditions, this case can be viewed as a new way for the distillation of coherent state. These interesting results of coherence transformation will give us a better understanding of the resource manipulation.
Coherence-assisted transformation under incoherent operations is discussed. For transformation from the pure state to the mixed state, we show that the coherence loss can be partially recovered by adding auxiliary coherent states. First, we discuss the coherence-assisted transformation for qubit states and give the sufficient and necessary condition for the partial recovery of coherence loss, and the maximum of the recovery of coherence loss is also studied in this case. Second, the maximally coherent state can be obtained in the above recovery scheme, so we give the full characterization of obtaining the maximally coherent state in a qubit system. Finally, we show that the coherence-assisted transformation for arbitrary finite-dimensional main coherent states and low-dimensional auxiliary coherent states is always possible, and the coherence loss also can be partially recovered in these cases.
We introduce and study the task of assisted coherence distillation. This task arises naturally in bipartite systems where both parties work together to generate the maximal possible coherence on one of the subsystems. Only incoherent operations are allowed on the target system, while general local quantum operations are permitted on the other; this is an operational paradigm that we call local quantum-incoherent operations and classical communication. We show that the asymptotic rate of assisted coherence distillation for pure states is equal to the coherence of assistance, an analog of the entanglement of assistance, whose properties we characterize. Our findings imply a novel interpretation of the von Neumann entropy: it quantifies the maximum amount of extra quantum coherence a system can gain when receiving assistance from a collaborative party. Our results are generalized to coherence localization in a multipartite setting and possible applications are discussed.
Abstract The coherence transformation and distillation for a class of special mixed coherent states of rank‐2 under incoherent operations (IO) is discussed. Similar to the entanglement transformation for mixed entangled states, the catalytic coherence transformation for this class of special mixed coherent states is analyzed. On the one hand, it is found that some of the mixed coherent states can be converted into other mixed coherent states under IO. But for those mixed coherent states which fail in the coherence conversion under IO, the catalytic coherence manipulation can solve this problem. In this case, a mixed coherent state cannot be converted into another under IO, while the coherence transformation can be realized with the help of coherence‐assisted incoherent operations, that is, catalytic coherence transformation. On the other hand, these special mixed coherent states can be distilled into the maximally pure coherent states or mixed states of arbitrary dimensions by strictly incoherent operations with certain probabilities. Finally, the coherence transformation of this type of mixed states can be generalized to the case of higher rank in a similar way, which is discussed at the end of this paper.
Coherence distillation is one of the central problems in the resource theory of coherence. In this Letter, we complete the deterministic distillation of quantum coherence for a finite number of coherent states under strictly incoherent operations. Specifically, we find the necessary and sufficient condition for the transformation from a mixed coherent state into a pure state via strictly incoherent operations, which recovers a connection between the resource theory of coherence and the algebraic theory of majorization lattice. With the help of this condition, we present the deterministic coherence distillation scheme and derive the maximum number of maximally coherent states obtained via this scheme.
Quantum state transformation under free operations plays a central role in the resource theory of coherence. In this paper, we investigate the transformation from a mixed coherent state into a pure one by using both incoherent operations and stochastic incoherent operations. We show that contrary to the strictly incoherent operations and the stochastic strictly incoherent operations, both the incoherent operations and the stochastic incoherent operations can increase the dimension of the maximal pure coherent subspace of a state. This means that the incoherent operations are generally stronger than the strictly incoherent operations when we want to transform a mixed coherent state into a pure coherent one. Our findings can also be interpreted as confirming the ability of incoherent operations to enhance the coherence of mixed states relative to certain coherence monotones under strictly incoherent operations.
The remarkable phenomenon of catalyst tells us that adding a catalyst could help state transformation. In this paper, we consider the problem of catalyst-assisted probabilistic coherence distillation for mixed states under strictly incoherent operations. To this end, we first present the necessary and sufficient conditions for distilling a target pure coherent state from an initial mixed state via stochastic strictly incoherent operations and the maximal probability of obtaining the target pure state from the initial state. With the help of these results, we present the necessary and sufficient conditions for the existence of a catalyst that increases the maximal transformation probability.