Xian Shi

We investigate resource nongenerating operations (RNOs) in both static and dynamical quantum resource theories. For the static scenarios, we derive a sufficient condition for state transformations under RNOs. Then we construct a dynamical resource theory where RNOs constitute the set of free operations, and we propose an axiomatic approach to quantify quantum channels. We further analyze the erasure of the dynamical resources. As applications, we establish bounds on the asymptotic cost of states under RNOs in a generic convex resource theory and obtain capacity bounds for communication tasks assisted by dynamical coherence. Our results clarify the key roles of RNOs in quantum information processing tasks.

Quantum state discrimination is a fundamental task that is meaningful in quantum information theory. In this manuscript, we consider an extended unambiguous discrimination of quantum resources. First, we present an upper bound of the success probability for an extended unambiguous discrimination task in the non-asymptotic and asymptotic scenarios. Next, we generalize the task from quantum states to quantum channels. We present an upper bound of the success probability for the task under the adaptive strategy. Furthermore, we show the bound can be computed efficiently. Finally, compared with the classical generalized unambiguous discrimination, we show the advantage of the quantum with the aid of a quantifier based on a set of semi-definite positive operators.

Quantum state discrimination is a fundamental task that is meaningful in quantum information theory. In this manuscript, we consider a revised unambiguous discrimination of quantum resources. First, we present an upper bound of the success probability for a revised unambiguous discrimination task in the unasymptotic and asymptotic scenarios. Next, we generalize the task from quantum states to quantum channels. We present an upper bound of the success probability for the task under the adaptive strategy. Furthermore, we show the bound can be computed efficiently. Finally, compared with the classical unambiguous discrimination, we show the advantage of the quantum by considering a quantifier on a set of semidefinite positive operators.

Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with a Schmidt number less than k.

In this work, we present a coherence measure based on the quantum optimal transport cost in terms of the convex roof extended method. We also obtain the analytical solutions of the quantifier for pure states. We also propose an operational interpretation of the coherence measure for pure states.

Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. Schmidt number is a quantity on the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with Schmidt number less than k.