A simple formulation of no-cloning and no-hiding that admits efficient and robust verification

Abstract

Incompatibility is a feature of quantum theory that sets it apart from classical theory, and the inability to clone an unknown quantum state is one of the most fundamental instances. The no-hiding theorem is another such instance that arises in the context of the black-hole information paradox, and can be viewed as being dual to no-cloning. Here, we formulate both of these fundamental features of quantum theory in a single form that is amenable to efficient verification, and that is robust to errors arising in state preparation and measurements. We extend the notion of unitarity - an average figure of merit that for quantum theory captures the coherence of a quantum channel - to general physical theories. Then, we introduce the notion of compatible unitarity pair (CUP) sets, that correspond to the allowed values of unitarities for compatible channels in the theory. We show that a CUP-set constitutes a simple 'fingerprint' of a physical theory, and that incompatibility can be studied through them. We derive information-disturbance constraints on quantum CUP-sets that encode both the no-cloning/broadcasting and no-hiding theorems of quantum theory. We then develop randomised benchmarking protocols that efficiently estimate quantum CUP-sets and provide simulations using IBMQ of the simplest instance. Finally, we discuss ways in which CUP-sets and quantum no-go theorems could provide additional information to benchmark quantum devices.

arXiv comment27 pages, 11 figures; comments welcome!

References in corpus (54)

• Quantum Computing in the NISQ era and beyond
• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Significant-loophole-free test of Bell's theorem with entangled photons
• A strong loophole-free test of local realism
• Quantum fingerprinting
• Randomized Benchmarking of Quantum Gates
• On quantum Renyi entropies: a new generalization and some properties
• Optimal Quantum Cloning Machines
• Noncommuting mixed states cannot be broadcast
• Quantum cloning
• Optimal Universal and State-Dependent Quantum Cloning
• Noise tailoring for scalable quantum computation via randomized compiling
• Probabilistic theories with purification
• Optimal Quantum Circuits for General Two-Qubit Gates
• Efficient measurement of quantum gate error by interleaved randomized benchmarking
• The randomized measurement toolbox
• Quantum certification and benchmarking
• A generalized no-broadcasting theorem
• An Invitation to Quantum Incompatibility
• Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox
• Estimating the Coherence of Noise
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• Quantum from principles
• Quasi-quantization: classical statistical theories with an epistemic restriction
• The completeness of quantum theory for predicting measurement outcomes
• Single-shot fault-tolerant quantum error correction
• Generalized Probability Theories: What determines the structure of quantum theory?
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Theory of quantum system certification: a tutorial
• Quantum Cloning Machines and the Applications
• Quantum information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit
• Quantum Incompatibility Witnesses
• General probabilistic theories: An introduction
• Masking quantum information is impossible
• Incompatibility robustness of quantum measurements: a unified framework
• Robustness of incompatibility for quantum devices
• Hiding and masking quantum information in complex and real quantum mechanics
• Incompatibility of quantum channels
• Optimal two-qubit quantum circuits using exchange interactions
• Coherifying quantum channels
• Bounding the average gate fidelity of composite channels using the unitarity
• Experimental Test of Quantum No-Hiding Theorem
• Monogamy of correlations and entropy inequalities in the Bloch picture
• Incompatible measurements in a class of general probabilistic theories
• Witnessing incompatibility of quantum channels
• Jordan products of quantum channels and their compatibility
• Demonstration of the No-Hiding Theorem on the 5 Qubit IBM Quantum Computer in a Category Theoretic Framework
• Incompatibility in general probabilistic theories, generalized spectrahedra, and tensor norms
• Spectral Quantum Tomography
• Robustness of Noether's principle: Maximal disconnects between conservation laws and symmetries in quantum theory
• Extremal asymmetric universal cloning machines
• Estimation of correlations and non-separability in quantum channels via unitarity benchmarking
• A Fisher information-based incompatibility criterion for quantum channels
• Partial randomized benchmarking