Abstract
We present an optimal probabilistic protocol to distill quantum coherence. Inspired by a specific entanglement distillation protocol, our main result yields a strictly incoherent operation that produces one of a family of maximally coherent states of variable dimension from any pure quantum state. We also expand this protocol to the case where it is possible, for some initial states, to avert any waste of resources as far as the output states are concerned, by exploiting an additional transformation into a suitable intermediate state. These results provide practical schemes for efficient quantum resource manipulation.
Highlights
Over the past three decades quantum entanglement has been identified as one of the main resources that allows us to overcome the intrinsic limits of classical information processing in a distributed setting [1]
We introduce an explicit protocol for coherence distillation via a single strictly incoherent operation where we originally have a d-level coherent input state; see Fig. 1
The entire transformation |φ → |φ → {pq, | q }q=2,...,d may provide no complete waste of resources, it may lead to a decreased amount of the largest distilled entanglement
Summary
Over the past three decades quantum entanglement has been identified as one of the main resources that allows us to overcome the intrinsic limits of classical information processing in a distributed setting [1]. The problem of distilling as much entanglement as possible from a given pure state by means of a probabilistic protocol using local operations and classical communication was considered in Refs. Quantum coherence plays an essential role in applications to quantum algorithms, quantum metrology, and quantum biology [9] To deal with this point of view, a resource theory of quantum coherence has been recently established [9,10,11,12,13]. We introduce an explicit protocol for coherence distillation via a single strictly incoherent operation where we originally have a d-level coherent input state; see Fig. 1. This strategy is a counterpart to the entanglement distillation given in Refs. We complement our analysis with a quantification of the coherence loss on average in our protocol, and comment on how and for which input states it is possible to modify our strategy, to avoid any waste of resources and always output a state with nonzero coherence
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