Virtual quantum resource distillation

Abstract

Distillation, or purification, is central to the practical use of quantum resources in noisy settings often encountered in quantum communication and computation. Conventionally, distillation requires using some restricted 'free' operations to convert a noisy state into one that approximates a desired pure state. Here, we propose to relax this setting by only requiring the approximation of the measurement statistics of a target pure state, which allows for additional classical postprocessing of the measurement outcomes. We show that this extended scenario, which we call virtual resource distillation, provides considerable advantages over standard notions of distillation, allowing for the purification of noisy states from which no resources can be distilled conventionally. We show that general states can be virtually distilled with a cost (measurement overhead) that is inversely proportional to the amount of existing resource, and we develop methods to efficiently estimate such cost via convex and semidefinite programming, giving several computable bounds. We consider applications to coherence, entanglement, and magic distillation, and an explicit example in quantum teleportation (distributed quantum computing). This work opens a new avenue for investigating generalized ways to manipulate quantum resources.

6 pages, 2 figures; See also the companion paper arXiv:2404.13048 for the broader framework and complete technical proofs

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Cited by in corpus (18)

• Optimal joint cutting of two-qubit rotation gates
• Virtual quantum resource distillation: General framework and applications
• Uniqueness of quantum state over time function
• Dynamical Landauer Principle: Quantifying Information Transmission by Thermodynamics
• Experimental virtual distillation of entanglement and coherence
• Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information
• Cutting a Wire with Non-Maximally Entangled States
• Dynamical Landauer principle: Thermodynamic criteria of transmitting classical information
• Shadow Simulation of Quantum Processes
• Experimental Virtual Quantum Broadcasting
• Joint Wire Cutting with Non-Maximally Entangled States
• Power of quantum measurement in simulating unphysical operations
• Readout Error Mitigation for Mid-Circuit Measurements and Feedforward
• No Practical Quantum Broadcasting: Even Virtually
• Experimental Quantum Channel Purification
• Virtual Quantum Markov Chains
• Virtual Cloning of Quantum States
• Noisy Monitored Quantum Circuits