Quantum Bayes rule
arXiv:quant-ph/0008113 · doi:10.1103/PhysRevA.64.014305
Abstract
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state of the N copies is exchangeable. As an illustration, we apply the rule to N qubits. Finally, we show that quantum state estimates derived via the principle of maximum entropy are fundamentally different from those obtained via the quantum Bayes rule.
REVTEX, 9 pages
References in corpus (2)
Cited by in corpus (67)
- Quantum probabilities as Bayesian probabilities
- Unknown Quantum States: The Quantum de Finetti Representation
- Optimal, reliable estimation of quantum states
- Quantum Mechanics as Quantum Information (and only a little more)
- Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
- Quantum-Bayesian Coherence: The No-Nonsense Version
- QBism, the Perimeter of Quantum Bayesianism
- Reliable Quantum State Tomography
- Quasi-probability representations of quantum theory with applications to quantum information science
- Optimizing quantum process tomography with unitary 2-designs
- Quantum Foundations in the Light of Quantum Information
- Practical Bayesian Tomography
- A Quantum-Bayesian Route to Quantum-State Space
- The Quantum State of an Ideal Propagating Laser Field
- Experimental Polarization State Tomography using Optimal Polarimeters
- Random Bures mixed states and the distribution of their purity
- Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements
- From time-reversal symmetry to quantum Bayes' rules
- Incomplete quantum state estimation: a comprehensive study
- A de Finetti Representation Theorem for Quantum Process Tomography
- Quantum theory from four of Hardy's axioms
- On quantum vs. classical probability
- Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces
- The Entropic Dynamics approach to Quantum Mechanics
- Von Neumann Was Not a Quantum Bayesian
- QBism: Quantum Theory as a Hero's Handbook
- Quantum estimation via minimum Kullback entropy principle
- Quantum key distribution rates from semidefinite programming
- Coherent States and Bayesian Duality
- Simulation of complex dynamics of mean-field -spin models using measurement-based quantum feedback control
- Quantum mechanics: The Bayesian theory generalised to the space of Hermitian matrices
- Quantum Model Averaging
- On determining which quantum measurement performs better for state estimation
- Entropic Updating of Probability and Density Matrices
- Mobius operators and non-additive quantum probabilities in the Birkhoff-von Neumann lattice
- Coherent chemical kinetics as quantum walks I: Reaction operators for radical pairs
- Subjective and Objective Probabilities in Quantum Mechanics
- Experimental quantum tomography assisted by multiply symmetric states in higher dimensions
- Tomography scheme for two spin-1/2 qubits in a double quantum dot
- Conditional expectation and Bayes' rule for quantum random variables and positive operator valued measures
- Error probability analysis in quantum tomography: a tool for evaluating experiments
- Adaptive estimation of qubits by symmetry measurements
- Compatibility of quantum states
- Inferring the Gibbs state of a small quantum system
- Lower and upper probabilities in the distributive lattice of subsystems
- Ideas Abandoned en Route to QBism
- Algorithmic Information Theoretic Issues in Quantum Mechanics
- Quantum Bayes' rule and Petz transpose map from the minimum change principle
- Quantum Annealing for Variational Bayes Inference
- Quantum Bayesian methods and subsequent measurements
- Coarse graining the phase space of qubits
- Lüders' and quantum Jeffrey's rules as entropic projections
- Bayesian Generalized Probability Calculus for Density Matrices
- Quantum and Classical Bayesian Agents
- Optical homodyne detection in view of joint probability distribution
- The Inferential Design of Entropy and its Application to Quantum Measurements
- Numerical Bayesian state assignment for a three-level quantum system. I. Absolute-frequency data; constant and Gaussian-like priors
- Assessing thermalization and estimating the Hamiltonian with output data only
- Appearance of Gibbs states in quantum-state tomography
- A de Finetti theorem for quantum causal structures
- Proper and improper mixed states serve as different prior beliefs for quantum state retrodiction
- Quantum Conditional Probabilities and New Measures of Quantum Information
- On distinguishability, orthogonality, and violations of the second law: contradictory assumptions, contrasting pieces of knowledge
- QBians Do Not Exist
- Reasoning about quantum systems at the macroscopic level
- Comparing weak and projective measurements for quantum state tomography of a single-qubit system
- Coarse-graining in retrodictive quantum state tomography