Data-Driven Inference, Reconstruction, and Observational Completeness of Quantum Devices
arXiv:1812.08470 · doi:10.1103/PhysRevA.102.062407
Abstract
The range of a quantum measurement is the set of outcome probability distributions that can be produced by varying the input state. We introduce data-driven inference as a protocol that, given a set of experimental data as a collection of outcome distributions, infers the quantum measurement which is, i) consistent with the data, in the sense that its range contains all the distributions observed, and, ii) maximally noncommittal, in the sense that its range is of minimum volume in the space of outcome distributions. We show that data-driven inference is able to return a unique measurement for any data set if and only if the inference adopts a (hyper)-spherical state space (for example, the classical or the quantum bit). In analogy to informational completeness for quantum tomography, we define observational completeness as the property of any set of states that, when fed into any given measurement, produces a set of outcome distributions allowing for the correct reconstruction of the measurement via data-driven inference. We show that observational completeness is strictly stronger than informational completeness, in the sense that not all informationally complete sets are also observationally complete. Moreover, we show that for systems with a (hyper)-spherical state space, the only observationally complete simplex is the regular one, namely, the symmetric informationally complete set.
arXiv comment15 pages, 12 figures, published version
References in corpus (25)
- Symmetric Informationally Complete Quantum Measurements
- In defense of the epistemic view of quantum states: a toy theory
- Informational derivation of Quantum Theory
- Non-local correlations as an information theoretic resource
- The Physics and Mathematics of the Second Law of Thermodynamics
- Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
- Quantum Theory From Five Reasonable Axioms
- An Introduction to QBism with an Application to the Locality of Quantum Mechanics
- Measuring measurement
- Quantum-Bayesian Coherence: The No-Nonsense Version
- A derivation of quantum theory from physical requirements
- Tomography of Quantum Operations
- The SIC Question: History and State of Play
- Maximum-likelihood estimation of quantum measurement
- Measuring Measurement: Theory and Practice
- Clean Positive Operator Valued Measures
- Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes
- Comparison of quantum statistical models: equivalent conditions for sufficiency
- Quantum Relative Lorenz Curves
- Relative submajorization and its use in quantum resource theories
- Optimal quantum tomography for states, measurements, and transformations
- Comparison of Information Structures and Completely Positive Maps
- Device-independent tests of quantum measurements
- Testing axioms for Quantum Mechanics on Probabilistic toy-theories
- Data-Driven Inference of Physical Devices: Theory and Implementation