Projective robustness for quantum channels and measurements and their operational significance

Abstract

Recently, the projective robustness of quantum states has been introduced in [arXiv:2109.04481(2021)]. It shows that the projective robustness is a useful resource monotone and can comprehensively characterize capabilities and limitations of probabilistic protocols manipulating quantum resources deterministically. In this paper, we will extend the projective robustness to any convex resource theories of quantum channels and measurements. First, We introduce the projective robustness of quantum channels and prove that it satisfies some good properties, especially sub- or supermultiplicativity under any free quantum process. Moreover, we use the projective robustness of channels to give lower bounds on the errors and overheads in any channel resource distillation. Meanwhile, we show that the projective robustness of channels quantifies the maximal advantage that a given channel outperforms all free channels in simultaneous discrimination and exclusion of a fixed state ensemble. Second, we define the projective robustness of quantum measurements and prove that it exactly quantifies the maximal advantage that a given measurement provides over all free measurements in simultaneous discrimination and exclusion of two fixed state ensembles. Finally, within a specific channel resource setting based on measurement incompatibility, we show that the projective robustness of quantum channels coincides with the projective robustness of measurement incompatibility.

12 pages

References in corpus (18)

• Application of a resource theory for magic states to fault-tolerant quantum computing
• Transforming quantum operations: quantum supermaps
• Quantifying Superposition
• All sets of incompatible measurements give an advantage in quantum state discrimination
• One-Shot Operational Quantum Resource Theory
• Operational relevance of resource theories of quantum measurements
• Quantum Relative Lorenz Curves
• Dynamical Entanglement
• Fundamental limitations on distillation of quantum channel resources
• Probabilistic transformations of quantum resources
• No-go theorems for quantum resource purification II: new approach and channel theory
• Resource theories of quantum channels and the universal role of resource erasure
• Operational quantification of continuous-variable quantum resources
• Framework for resource quantification in infinite-dimensional general probabilistic theories
• One-Shot Manipulation of Dynamical Quantum Resources
• Tight constraints on probabilistic convertibility of quantum states
• Multi-object operational tasks for convex quantum resource theories
• One-shot manipulation of entanglement for quantum channels