Strictly incoherent operations for one-qubit systems

Abstract

Strictly incoherent operations (SIO) proposed in Winter and Yang (2016) [13] are promising to be a good candidate of free operations in the resource theory of quantum coherence, setting against the central role of local operations and classical communication in the resource theory of quantum entanglement. An important open problem for SIOs is to find minimal parametrization with operational efficiency. Such a description plays key role for axiomatic study of resource theory of quantum coherence. We are aimed to give a structural characterization of bistochastic SIOs in terms of Pauli operators and the Phase operator for one-qubit systems. Some applications of our results are also sketched in reconstructing quantum thermal averages via a quantum computer and in coherence manipulation.