Operational framework for quantum measurement simulability

Abstract

We introduce a framework for simulating quantum measurements based on classical processing of a set of accessible measurements. Well-known concepts such as joint measurability and projective simulability naturally emerge as particular cases of our framework, but our study also leads to novel results and questions. First, a generalisation of joint measurability is derived, which yields a hierarchy for the incompatibility of sets of measurements. A similar hierarchy is defined based on the number of outcomes used to perform the simulation of a given measurement. This general approach also allows us to identify connections between different types of simulability and, in particular, we characterise the qubit measurements that are projective-simulable in terms of joint measurability. Finally, we discuss how our framework can be interpreted in the context of resource theories.

25 pages, single-column, 3 figures. Closer to published version

References in corpus (12)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• The resource theory of quantum reference frames: manipulations and monotones
• Bloch vectors for qudits
• Joint measurability of generalized measurements implies classicality
• Simulating positive-operator-valued measures with projective measurements
• The WAY theorem and the quantum resource theory of asymmetry
• Clean Positive Operator Valued Measures
• Notes on Joint Measurability of Quantum Observables
• Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$
• Commutative POVMs and Fuzzy Observables
• Most incompatible measurements for robust steering tests

Cited by in corpus (52)

• Quantum Resource Theories
• Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Quantifying quantum resources with conic programming
• All sets of incompatible measurements give an advantage in quantum state discrimination
• Incompatible measurements in quantum information science
• Robustness of Measurement, discrimination games and accessible information
• Self-testing non-projective quantum measurements in prepare-and-measure experiments
• Operational relevance of resource theories of quantum measurements
• A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
• Quantum measurement incompatibility does not imply Bell nonlocality
• Application of the Resource Theory of Channels to Communication Scenarios
• Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states
• Simulating all quantum measurements using only projective measurements and postselection
• Simulability of observables in general probabilistic theories
• Contextuality without incompatibility
• Simulability of high-dimensional quantum measurements
• Implementation of quantum measurements using classical resources and only a single ancillary qubit
• A Resource Theory of Quantum Measurements
• Multi-object operational tasks for convex quantum resource theories
• No-free-information principle in general probabilistic theories
• Every quantum helps: Operational advantage of quantum resources beyond convexity
• Operational restrictions in general probabilistic theories
• Characterisation of quantum betting tasks in terms of Arimoto mutual information
• Incompatibility as a resource for programmable quantum instruments
• How much randomness can be generated from a quantum black-box device?
• Operational foundations of complementarity and uncertainty relations
• Post-processing of quantum instruments
• A general theory of comparison of quantum channels (and beyond)
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• Multiple-shot and unambiguous discrimination of von Neumann measurements
• Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios
• Distance-based resource quantification for sets of quantum measurements
• Compact convex structure of measurements and its applications to simulability, incompatibility, and convex resource theory of continuous-outcome measurements
• Distributed quantum incompatibility
• Relating compatibility and divisibility of quantum channels
• Noise-disturbance relation and the Galois connection of quantum measurements
• Random access test as an identifier of nonclassicality
• Simulating quantum instruments with projective measurements and quantum post-processing
• Anticipative measurements in hybrid quantum-classical computation
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Projective robustness for quantum channels and measurements and their operational significance
• Entropic partial orderings of quantum measurements
• Finite-Dimensional Convex Effect Algebras
• Retrodiction of measurement outcomes on a single quantum system reveals entanglement with its environment
• Multi-object operational tasks for measurement incompatibility
• Cost of Simulating Entanglement in Steering Scenario
• Can a qudit carry more information than a dit?
• Encoding and decoding of information in general probabilistic theories
• Classifying Measurement Incompatibility under Classical Pre- and Post-Processing Operations
• Semi-device-independent certification of number of measurements
• On the simulation of quantum multimeters