Quantum Bayes rule

By Ruediger Schack, Todd A. Brun, Carlton M. Caves. 2000

138 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/37f6ac3515bc8024e9d5ed49d3e0273abccac268

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Unknown Quantum States and Operations, a Bayesian View (2004, unknown): “where P (ρ|α) is given by a quantum Bayes rule [2].”
Quantum Mechanics as Quantum Information (and only a little more) (2002, background): “It guarantees for two independent observers—as long as they have a rather minimal agreement in their initial beliefs—that the outcomes of a sufficiently informative set of measurements will force a convergence in their state assignments for the remaining systems [33].”
QBism, the Perimeter of Quantum Bayesianism (2010, background): “performs tomography, all he is doing is gathering data system-by-system and updating, via Bayes rule [25], the state ρ to some new state ρ on a smaller number of remaining systems.”
Quasi-probability representations of quantum theory with applications to quantum information science (2010, background): “Quantum Bayesianism (Caves et al 2002a, Fuchs 2002, Fuchs 2010, Fuchs and Schack 2009, Schack et al 2001) is an interpretation of quantum theory which sheds new light on not only the tradition ‘foundational’ problems (the ‘measurement problem’, for example) but also many concepts in quantum theory,…”
Quantum-Bayesian Coherence (2009, background): “Among the various arguments the Quantum Bayesians use to come to this conclusion, not least in importance is a thoroughgoing personalist account of all probabilities (Bernardo, 1994; de Finetti, 1931, 1990; Jeffrey, 2004; Ramsey, 1931; Savage, 1954)—where the “all” in this sentence includes probabil”
Unknown Quantum States: The Quantum de Finetti Representation (2001, background): “3) is a kind of quantum Bayes rule [40].”
A Quantum-Bayesian Route to Quantum-State Space (2009, background): “Maybe even more importantly, the success of this approach provides a compelling case for quantum Bayesianism [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12].”
Optimizing quantum process tomography with unitary 2-designs (2007, methodology): “We will call ρ̂ a linear tomographic estimate of ρ to distinguish it from more sophisticated choices, such as those from maximum likelihood estimation [17, 18] or Bayesian mean estimation [19–23].”
On Participatory Realism (2016, background): “Johannes Kofler said recently to Rüdiger Schack, “I am convinced we are biological machines.””
Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators (2012, methodology): “Most prior work on error bounds used either standard resampling techniques or Bayesian methods [42, 43, 45, 48, 50, 52].”
Quantum probabilities as Bayesian probabilities (2001, methodology): “The updating can be cast as an application of Bayes’s rule to updating the generating function in light of the data [21].”