All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources

Abstract

Which quantum phenomena are advantageous for information processing tasks? By classifying quantum states as resourceful versus non-resourceful, or free, the mathematical formalism of quantum resource theories helps to address such questions. For the task of discriminating channels applied to a probe state, it has been shown that under certain conditions -- namely, the set of free states being convex or finite dimensional -- every resourceful probe state can provide an advantage, quantified by a resource monotone known as generalized robustness. In this work, bypassing the limitations of previous studies, we define the generalized robustness for an arbitrary resource theory and show that it admits two operational interpretations. Firstly, it provides an upper bound on the maximal advantage in channel discrimination tasks implemented on multiple copies of the probe states. Secondly, in many physically relevant theories, it quantifies the advantage in single-copy channel discrimination tasks in a worst case scenario. We further present a general construction of multi-copy resource witnesses and provide practical methods to bound the generalized robustness in experiments. Finally, we apply our results to a key case study in continuous variable quantum information: the resource theory of non-Gaussianity. This theory is naturally defined by a set of free states (Gaussian states) that is non-convex and infinite-dimensional. Our work then shows conclusively that all non-Gaussian states can provide an advantage in some channel discrimination task, even those that are simply mixtures of Gaussian states and are typically disregarded for other quantum information tasks. To illustrate our findings, we provide exact formulas for the robustness of non-Gaussianity of Fock states, along with an analysis of the robustness for a family of non-Gaussian states within the convex hull of Gaussian states.

arXiv comment15 pages, 4 figures. Published version

References in corpus (61)

• Quantum entanglement
• Quantum information with continuous variables
• Gaussian Quantum Information
• Separability of Mixed States: Necessary and Sufficient Conditions
• Quantum Coherence as a Resource
• Quantum Resource Theories
• Advances in Photonic Quantum Sensing
• Continuous variable quantum information: Gaussian states and beyond
• On the impossibility of distilling Gaussian states with Gaussian operations
• Robustness of coherence: An operational and observable measure of quantum coherence
• The characterization of Gaussian operations and Distillation of Gaussian States
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Positive Wigner functions render classical simulation of quantum computation efficient
• Continuous-variable teleportation improvement by photon subtraction via conditional measurement
• Experimental realisation of quantum illumination
• Gaussian transformations and distillation of entangled Gaussian states
• Measures and applications of quantum correlations
• The general structure of quantum resource theories
• A No-Go Theorem for Gaussian Quantum Error Correction
• Extremality of Gaussian quantum states
• Non-Gaussian Quantum States and Where to Find Them
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
• Continuous variable quantum teleportation with non-Gaussian resources
• Quantifying non-Gaussianity for quantum information
• Quantum Reading of a Classical Digital Memory
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• Convex resource theory of non-Gaussianity
• Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states
• A measure of the non-Gaussian character of a quantum state
• Genralized Robustness of Entanglement
• Operational Advantage of Quantum Resources in Subchannel Discrimination
• On the quantification of entanglement in infinite-dimensional quantum systems
• Detecting quantum non-Gaussianity via the Wigner function
• Stellar representation of non-Gaussian quantum states
• Gaussian quantum resource theories
• Gaussian hypothesis testing and quantum illumination
• The Classification of Decoherence Functionals: An Analogue of Gleason's Theorem
• On Variational Expressions for Quantum Relative Entropies
• Relative entropy is an exact measure of non-Gaussianity
• Quantifying resource in catalytic resource theory
• Resources for bosonic quantum computational advantage
• Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states
• Operational quantification of continuous-variable quantum resources
• Framework for resource quantification in infinite-dimensional general probabilistic theories
• Quantum non-Gaussianity of light and atoms
• Experimental quantum reading with photon counting
• Enhancement of parameter estimation by Kerr interaction
• Key distillation from Gaussian states by Gaussian operations
• All phase-space linear bosonic channels are approximately Gaussian dilatable
• Every quantum helps: Operational advantage of quantum resources beyond convexity
• Quantifying non-Gaussianity of a quantum state by the negative entropy of quadrature distributions
• Characterisation of quantum betting tasks in terms of Arimoto mutual information
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• The strong converse exponent of discriminating infinite-dimensional quantum states
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• Resource engines
• Continuity of robustness measures in quantum resource theories
• Fundamental limitations to key distillation from Gaussian states with Gaussian operations
• Resource distillation in convex Gaussian resource theories