Causality in Higher Order Process Theories
arXiv:2107.14581 · doi:10.4204/EPTCS.343.12
Abstract
Quantum supermaps provide a framework in which higher order quantum processes can act on lower order quantum processes. In doing so, they enable the definition and analysis of new quantum protocols and causal structures. Recently, key features of quantum supermaps were captured through a general categorical framework, which led to a framework of higher order process theories (HOPT). The HOPT framework models lower and higher order transformations in a single unified theory, with its mathematical structure shown to coincide with the notion of a closed symmetric monoidal category. Here we provide an equivalent construction of the HOPT framework from four simple axioms of process-theoretic nature. We then use the HOPT framework to establish connections between foundational features such as causality, determinism and signalling, alongside exploring their interaction with the mathematical structure of *-autonomy.
arXiv commentIn Proceedings QPL 2021, arXiv:2109.04886
References in corpus (44)
- Quantum correlations with no causal order
- Quantum computations without definite causal structure
- Probabilistic theories with purification
- Quantum Circuits Architecture
- Transforming quantum operations: quantum supermaps
- Interacting Quantum Observables: Categorical Algebra and Diagrammatics
- A mathematical theory of resources
- A generalized no-broadcasting theorem
- Computational advantage from quantum-controlled ordering of gates
- Enhanced communication with the assistance of indefinite causal order
- Perfect discrimination of no-signalling channels via quantum superposition of causal structures
- Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication
- A Lambda Calculus for Quantum Computation
- Quantum Picturalism
- Quantum Metrology with Indefinite Causal Order
- Operational Resource Theory of Quantum Channels
- Indefinite causal order enables perfect quantum communication with zero capacity channels
- Optimal estimation of group transformations using entanglement
- Phase groups and the origin of non-locality for qubits
- Communication through coherent control of quantum channels
- Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard problems?
- Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations
- Causal categories: relativistically interacting processes
- Resource theories of communication
- Communication Enhancement Through Quantum Coherent Control of Channels in an Indefinite Causal-order Scenario
- Sending classical information via three noisy channels in superposition of causal orders
- Quartic quantum theory: an extension of the standard quantum mechanics
- Theoretical framework for Higher-Order Quantum Theory
- Dynamics of quantum causal structures
- Causal structures and the classification of higher order quantum computations
- Reconstructing quantum theory from diagrammatic postulates
- Classical Communications with Indefinite Causal Order for completely depolarizing channels
- Leaks: quantum, classical, intermediate, and more
- Maximum likelihood estimation for a group of physical transformations
- Infinite-dimensional Categorical Quantum Mechanics
- Success-or-Draw: A Strategy Allowing Repeat-Until-Success in Quantum Computation
- Open Diagrams via Coend Calculus
- Consequences of preserving reversibility in quantum superchannels
- Space in Monoidal Categories
- Routed quantum circuits
- Towards Quantum Field Theory in Categorical Quantum Mechanics
- Time-asymmetry of probabilities versus relativistic causal structure: an arrow of time
- Comb Diagrams for Discrete-Time Feedback
- Quantum Field Theory in Categorical Quantum Mechanics