The first law of general quantum resource theories

Sparaciari, Carlo; Rio, Lídia del; Scandolo, Carlo Maria; Faist, Philippe; Oppenheim, Jonathan

doi:10.22331/q-2020-04-30-259

Cited by 50 publications

(38 citation statements)

References 84 publications

(189 reference statements)

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“…Moreover, given that we have multiple different ways to define the partitioned process theory, then it would be worth exploring the basic mathematical structure of this as a play ground for defining resource theories with multiple different resources. This should have connections to the work of [79,80]. Indeed, section 4.5 can be viewed as preliminary work in this direction -at least for the case of decoherence.…”

Section: Future Workmentioning

confidence: 76%

Compositional resource theories of coherence

Selby

Lee

2020

Quantum

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Quantum coherence is one of the most important resources in quantum information theory. Indeed, preventing the loss of coherence is one of the most important technical challenges obstructing the development of large-scale quantum computers. Recently, there has been substantial progress in developing mathematical resource theories of coherence, paving the way towards its quantification and control. To date however, these resource theories have only been mathematically formalised within the realms of convex-geometry, information theory, and linear algebra. This approach is limited in scope, and makes it difficult to generalise beyond resource theories of coherence for single system quantum states. In this paper we take a complementary perspective, showing that resource theories of coherence can instead be defined purely compositionally, that is, working with the mathematics of process theories, string diagrams and category theory. This new perspective offers several advantages: i) it unifies various existing approaches to the study of coherence, for example, subsuming both speakable and unspeakable coherence; ii) it provides a general treatment of the compositional multi-system setting; iii) it generalises immediately to the case of quantum channels, measurements, instruments, and beyond rather than just states; iv) it can easily be generalised to the setting where there are multiple distinct sources of decoherence; and, iv) it directly extends to arbitrary process theories, for example, generalised probabilistic theories and Spekkens toy model---providing the ability to operationally characterise coherence rather than relying on specific mathematical features of quantum theory for its description. More importantly, by providing a new, complementary, perspective on the resource of coherence, this work opens the door to the development of novel tools which would not be accessible from the linear algebraic mind set.

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Section: Future Workmentioning

confidence: 76%

Compositional resource theories of coherence

Selby

Lee

2020

Quantum

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“…The constant term in (16) comes from the charges' noncommutation. The constant depends on the parameters that quantify how much the definition of "microcanonical subspace" is relaxed to include M. The larger the whole system, the better the (Q tot α /N )'s commute, so the less the definition needs relaxing, so the greater the probability that some M corresponds to a smaller constant.…”

Section: Proposal For Spin-chain Experimentsmentioning

confidence: 99%

“…The NATS theory predicts ρS with greater accuracy, which grows with the spin-chain size, for finite systems. The dotted line represents the best fit of the form of the prediction (16). Entropies are expressed in units of nats (not to be confused with the NATS: logarithms are base-e).…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…They govern the constants in Ineq. (16), the bound on the distance between ρ S and the NATS. The constants' forms are calculated partially in [7].…”

Section: Appendix a Protocol's Inequivalence To Thermalization Under mentioning

confidence: 99%

“…H S denotes the system-of-interest Hamiltonian, Q S α denotes the α th system-of-interest charge, the µ α 's denote generalized chemical potentials, and the partition function Z S NATS := Tr e −β(H S − α µαQ S α ) normalizes the state. This non-Abelian thermal state (NATS) (2) [7] has since spread across QI-theoretic thermodynamics [10][11][12][13][14][15][16].…”

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confidence: 99%

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Noncommuting conserved charges in quantum many-body thermalization

2020

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In statistical mechanics, a small system exchanges conserved charges-heat, particles, electric charge, etc.-with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the charges. The charges are usually represented by operators assumed to commute with each other. This assumption was removed within quantum-informationtheoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed "the non-Abelian thermal state (NATS)." We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which form the system of interest. The conserved charges manifest as spin components. Heisenberg interactions push the charges between the system and the effective bath, the rest of the chain. We predict longtime expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting charges from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.

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How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics

Halpern

Majidy

2022

npj Quantum Inf

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Noncommuting conserved quantities have recently launched a subfield of quantum thermodynamics. In conventional thermodynamics, a system of interest and an environment exchange quantities—energy, particles, electric charge, etc.—that are globally conserved and are represented by Hermitian operators. These operators were implicitly assumed to commute with each other, until a few years ago. Freeing the operators to fail to commute has enabled many theoretical discoveries—about reference frames, entropy production, resource-theory models, etc. Little work has bridged these results from abstract theory to experimental reality. This paper provides a methodology for building this bridge systematically: we present a prescription for constructing Hamiltonians that conserve noncommuting quantities globally while transporting the quantities locally. The Hamiltonians can couple arbitrarily many subsystems together and can be integrable or nonintegrable. Our Hamiltonians may be realized physically with superconducting qudits, with ultracold atoms, and with trapped ions.

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The first law of general quantum resource theories

Cited by 50 publications

References 84 publications

Compositional resource theories of coherence

Compositional resource theories of coherence

Noncommuting conserved charges in quantum many-body thermalization

How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics

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