Compositional resource theories of coherence

Abstract

Quantum coherence is one of the most important resources in quantum information. 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 go 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; 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.

arXiv comment43 pages, many diagrams, comments welcome! v2 -- new section on multiple sources of decoherence

References in corpus (64)

• Quantum entanglement
• Decoherence, einselection, and the quantum origins of the classical
• Quantifying Coherence
• Quantum Coherence as a Resource
• Quantum Resource Theories
• Conditions for a class of entanglement transformations
• Operational Resource Theory of Coherence
• In defense of the epistemic view of quantum states: a toy theory
• Informational derivation of Quantum Theory
• Quantum Darwinism
• Quantum coherence, time-translation symmetry and thermodynamics
• The resource theory of informational nonequilibrium in thermodynamics
• The general structure of quantum resource theories
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Interacting Quantum Observables: Categorical Algebra and Diagrammatics
• A mathematical theory of resources
• Relating the Resource Theories of Entanglement and Quantum Coherence
• (Quantumness in the context of) Resource Theories
• Enhanced communication with the assistance of indefinite causal order
• A quantitative theory of coherent delocalization
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Resource Destroying Maps
• Quantum processes which do not use coherence
• Operational Resource Theory of Quantum Channels
• Limited Holism and Real-Vector-Space Quantum Theory
• A resource theory of quantum memories and their faithful verification with minimal assumptions
• The WAY theorem and the quantum resource theory of asymmetry
• Towards resource theory of coherence in distributed scenarios
• How to quantify a dynamical quantum resource
• Phase groups and the origin of non-locality for qubits
• Operational relevance of resource theories of quantum measurements
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Quantum resource theories in the single-shot regime
• A Resource Theory for Work and Heat
• Towards device-independent information processing on general quantum networks
• Dynamical Resource Theory of Quantum Coherence
• Resource convertibility and ordered commutative monoids
• Generalised phase kick-back: the structure of computational algorithms from physical principles
• Ultimate data hiding in quantum mechanics and beyond
• Entanglement and thermodynamics in general probabilistic theories
• Entanglement is necessary for emergent classicality in all physical theories
• Entanglement is an inevitable feature of any non-classical theory
• Deriving Grover's lower bound from simple physical principles
• Computation in generalised probabilistic theories
• The computational landscape of general physical theories
• Thermodynamics and the structure of quantum theory
• Completely positive projections and biproducts
• Strong Complementarity and Non-locality in Categorical Quantum Mechanics
• Categorical Probabilistic Theories
• Microcanonical thermodynamics in general physical theories
• Entropy, majorization and thermodynamics in general probabilistic theories
• Oracles and query lower bounds in generalised probabilistic theories
• Quantum computation is the unique reversible circuit model for which bits are balls
• Leaks: quantum, classical, intermediate, and more
• Bounds on the power of proofs and advice in general physical theories
• Simple proof of the impossibility of bit-commitment in generalised probabilistic theories using cone programming
• How to make unforgeable money in generalised probabilistic theories
• Two Roads to Classicality
• Interferometric computation beyond quantum theory
• Agents, subsystems, and the conservation of information
• Nonclassicality without entanglement enables bit commitment
• A complete graphical calculus for Spekkens' toy bit theory
• The Information Content of Systems in General Physical Theories
• Device-independent certification of non-classical joint measurements via causal models

Cited by in corpus (6)

• Quantum work extraction efficiency for noisy quantum batteries: the role of coherence
• Inequalities witnessing coherence, nonlocality, and contextuality
• Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks
• Covariant influences for finite discrete dynamical systems
• Computation in a general physical setting
• CPM Categories for Galois Extensions