Probabilistic Coherence Transformation Under Strictly Incoherent Operation

An important problem in the coherent resource theory is the convertibility of coherent states by free operations. In this paper we consider such a problem from a mixed coherent state into a pure one by using both stochastic incoherent operations and incoherent operations. We prove that stochastic incoherent operations can transform a mixed coherent state into a pure coherent state if and only if the density matrix of the initial state contains a singular principal submatrix. Then we provide two sufficient conditions with explicit expressions for the probabilistic transformation and the deterministic transformation. These two sufficient conditions facilitate the construction of concrete operators of stochastic incoherent operations and incoherent operations. These results demonstrate that incoherent operations are strictly more powerful than strictly incoherent operations within the probabilistic transformation as well as the deterministic transformation.An important problem in the coherent resource theory is the convertibility of coherent states by free operations. In this paper we consider such a problem from a mixed coherent state into a pure one by using both stochastic incoherent operations and incoherent operations. We prove that stochastic incoherent operations can transform a mixed coherent state into a pure coherent state if and only if the density matrix of the initial state contains a singular principal submatrix. Then we provide two sufficient conditions with explicit expressions for the probabilistic transformation and the deterministic transformation. These two sufficient conditions facilitate the construction of concrete operators of stochastic incoherent operations and incoherent operations. These results demonstrate that incoherent operations are strictly more powerful than strictly incoherent operations within the probabilistic transformation as well as the deterministic transformation.

Physical Review AOct 16, 20234 citations

Optimal probabilistic distillation of quantum coherence

C. L. Liu, C. P. Sun

We complete the task of optimal probabilistic coherence distillation protocol, whose aim is to transform a general state into a set of $n$ -level maximally coherent states via strictly incoherent operations (SIO). Specifically, we present the necessary and sufficient condition for the transformation from a mixed state into a pure-state ensemble via SIO. With the aid of this condition and the simplex algorithm, we can accomplish the probabilistic distillation protocol by presenting an analytical expression of the maximal average distillable coherence of a general state and constructing the corresponding operation achieving this bound. Our protocol is a universal protocol since it can be applied to any coherence measure.We complete the task of optimal probabilistic coherence distillation protocol, whose aim is to transform a general state into a set of $n$-level maximally coherent states via strictly incoherent operations (SIO). Specifically, we present the necessary and sufficient condition for the transformation from a mixed state into a pure-state ensemble via SIO. With the aid of this condition and the simplex algorithm, we can accomplish the probabilistic distillation protocol by presenting an analytical expression of the maximal average distillable coherence of a general state and constructing the corresponding operation achieving this bound. Our protocol is a universal protocol since it can be applied to any coherence measure.

arXiv:2104.10990Physical Review ResearchDec 27, 202114 citations

Irreversible effects of random unitary transformations on coherence

Philippe Réfrégier, Alfredo Luis

Jan 1, 20080 citations

Catalyst-assisted probabilistic coherence distillation for mixed states

C. L. Liu, D. L. Zhou

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.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.

arXiv:2001.03508Physical Review AJan 10, 202030 citations

We complete the task of optimal probabilistic coherence distillation protocol, whose aim is to transform a general state into a set of

n

-level maximally coherent states via strictly incoherent operations (SIO). Specifically, we present the necessary and sufficient condition for the transformation from a mixed state into a pure-state ensemble via SIO. With the aid of this condition and the simplex algorithm, we can accomplish the probabilistic distillation protocol by presenting an analytical expression of the maximal average distillable coherence of a general state and constructing the corresponding operation achieving this bound. Our protocol is a universal protocol since it can be applied to any coherence measure.