Stochastic Coherence Theory for Qubits

TL;DR

This paper provides a complete solution for the optimal probabilistic conversion of mixed qubit states under incoherent operations, revealing fundamental limits and irreversibility in quantum coherence resource manipulation.

Contribution

It determines the optimal stochastic conversion probabilities for mixed qubits and establishes new bounds on asymptotic conversion rates, advancing coherence theory understanding.

Findings

Derived optimal probabilities for mixed qubit state conversions.

Established lower bounds on asymptotic coherence conversion rates.

Identified minimal distillable coherence for given coherence cost.

Abstract

The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and interconversion of this resource. Here we solve this question completely for mixed states of qubits by determining the optimal probabilities for mixed state conversions via stochastic incoherent operations. This implies new lower bounds on the asymptotic state conversion rate between mixed single-qubit states which in some cases is proven to be tight. Furthermore, we obtain the minimal distillable coherence for given coherence cost among all single-qubit states, which sheds new light on the irreversibility of coherence theory.