Memory cost of quantum contextuality

Abstract

The simulation of quantum effects requires certain classical resources, and quantifying them is an important step in order to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of state-independent quantum contextuality, we show that the minimal amount of memory used by the simulation is the critical resource. We derive optimal simulation strategies for important cases and prove that reproducing the results of sequential measurements on a two-qubit system requires more memory than the information carrying capacity of the system.

18 pages, no figures, v2: revised for clarity

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Cited by in corpus (53)

• Quantum Resource Theories
• Kochen-Specker Contextuality
• Dimension witnesses and quantum state discrimination
• Experimental Device-independent Tests of Classical and Quantum Dimensions
• Quantifying Contextuality
• State independent contextuality advances one-way communication
• Simple method for experimentally testing any form of quantum contextuality
• Robust self-testing of quantum systems via noncontextuality inequalities
• Sustained state-independent quantum contextual correlations from a single ion
• Contextuality without nonlocality in a superconducting quantum system
• Quantum contextuality provides communication complexity advantage
• Non-classicality of temporal correlations
• Leggett-Garg macrorealism and the quantum nondisturbance conditions
• Nonlocality from local contextuality
• Optimal classical simulation of state-independent quantum contextuality
• Necessary and sufficient condition for contextuality from incompatibility
• Axiomatic approach to contextuality and nonlocality
• Structure of temporal correlations of a qubit
• Classical Physics and the Bounds of Quantum Correlations
• One-Shot Manipulation of Dynamical Quantum Resources
• Using quantum theory to reduce the complexity of input-output processes
• Contextuality and Noncontextuality Measures and Generalized Bell Inequalities for Cyclic Systems
• Efficient classical simulation of the Deutsch-Jozsa and Simon's algorithms
• Experimental test of contextuality in quantum and classical systems
• Leggett-Garg Macrorealism and temporal correlations
• Memory cost of temporal correlations
• Memory cost for simulating all quantum correlations of the Peres-Mermin scenario
• Contextuality and The Single-Qubit Stabilizer Formalism
• Bounding and simulating contextual correlations in quantum theory
• Noncontextuality Inequalities from Antidistinguishability
• Quantum Simulation Logic, Oracles, and the Quantum Advantage
• Temporal correlations in the simplest measurement sequences
• Bell non-locality and Kochen-Specker contextuality: How are they connected?
• Simulating extremal temporal correlations
• Ticking-clock performance enhanced by nonclassical temporal correlations
• Classical systems can be contextual too: Analogue of the Mermin-Peres square
• Certifying the quantumness of a nuclear spin qudit through its uniform precession
• Corrected Bell and Noncontextuality Inequalities for Realistic Experiments
• Large violations in Kochen Specker contextuality and their applications
• The rank of contextuality
• Quantum correlations with a gap between the sequential and spatial cases
• Irreducible magic sets for $n$-qubit systems
• State-recycling method for testing contextuality
• A computational test of quantum contextuality, and even simpler proofs of quantumness
• Optimisation of time-ordered processes in the finite and asymptotic regime
• Analysis of single-particle nonlocality through the prism of weak measurements
• Measuring the Mermin-Peres magic square using an online quantum computer
• Exploring the boundary of quantum correlations with a time-domain optical processor
• Graph-theoretic approach to dimension witnessing
• Experimental Approach to Demonstrating Contextuality for Qudits
• How contextuality and antidistinguishability are related
• Quantum contextuality from measurement invasiveness
• Convexity of noncontextual wirings and how they order the set of correlations