Process tomography in general physical theories
arXiv:2109.12067 · doi:10.3390/sym13111985
Abstract
Process tomography, the experimental characterization of physical processes, is a central task in science and engineering. Here we investigate the axiomatic requirements that guarantee the in-principle feasibility of process tomography in general physical theories. Specifically, we explore the requirement that process tomography should be achievable with a finite number of auxiliary systems and with a finite number of input states. We show that this requirement is satisfied in every theory equipped with universal extensions, that is, correlated states from which all other correlations can be generated locally with non-zero probability. We show that universal extensions are guaranteed to exist in two cases: (1) theories permitting conclusive state teleportation, and (2) theories satisfying three properties of Causality, Pure Product States, and Purification. In case (2), the existence of universal extensions follows from a symmetry property of Purification, whereby all pure bipartite states with the same marginal on one system are locally interconvertible. Crucially, our results hold even in theories that do not satisfy Local Tomography, the property that the state of any composite system can be identified from the correlations of local measurements. Summarizing, the existence of universal extensions, without any additional requirement of Local Tomography, is a sufficient guarantee for the characterizability of physical processes using a finite number of auxiliary systems.
arXiv comment16 + 12 pages, new results added
References in corpus (41)
- Prescription for experimental determination of the dynamics of a quantum black box
- Complete Characterization of a Quantum Process: the Two-Bit Quantum Gate
- In defense of the epistemic view of quantum states: a toy theory
- Informational derivation of Quantum Theory
- Probabilistic theories with purification
- Quantum Process Tomography: Resource Analysis of Different Strategies
- Ancilla-assisted quantum process tomography
- A derivation of quantum theory from physical requirements
- Tomography of Quantum Operations
- A generalized no-broadcasting theorem
- Efficient measurement of quantum dynamics via compressive sensing
- Quantum from principles
- Quasi-quantization: classical statistical theories with an epistemic restriction
- Introduction to the book "Quantum Theory: Informational Foundations and Foils"
- The completeness of quantum theory for predicting measurement outcomes
- Quantum Picturalism
- Complete Characterization of Quantum-Optical Processes
- Optimizing quantum process tomography with unitary 2-designs
- Limited Holism and Real-Vector-Space Quantum Theory
- Higher-order interference and single-system postulates characterizing quantum theory
- Existence of an information unit as a postulate of quantum theory
- Choi's Proof and Quantum Process Tomography
- Quantum process tomography of unitary and near-unitary maps
- Causal categories: relativistically interacting processes
- Real-Vector-Space Quantum Theory with a Universal Quantum Bit
- Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation
- Entanglement Sharing in Real-Vector-Space Quantum Theory
- Quantum Theory, namely the pure and reversible theory of information
- Optimal quantum tomography for states, measurements, and transformations
- Quantum replication at the Heisenberg limit
- Fermionic computation is non-local tomographic and violates monogamy of entanglement
- Reconstructing quantum theory from diagrammatic postulates
- Dilation of states and processes in operational-probabilistic theories
- The rebit three-tangle and its relation to two-qubit entanglement
- Categorical Probabilistic Theories
- Microcanonical thermodynamics in general physical theories
- Operational axioms for diagonalizing states
- Composites and Categories of Euclidean Jordan Algebras
- Conjugates, Filters and Quantum Mechanics
- Fermionic state discrimination by local operations and classical communication
- Proceedings 14th International Conference on Quantum Physics and Logic