Quantum Systems, Information and Controlhttp://hdl.handle.net/2160/29722016-05-30T12:36:45Z2016-05-30T12:36:45ZA Noncommutative de Finetti Theorem: Invariance under Quantum Permutations is Equivalent to Freeness with AmalgamationKöstler, ClausSpeicher, Rolandhttp://hdl.handle.net/2160/424282016-03-24T15:11:37Z2009-12-31T00:00:00ZA Noncommutative de Finetti Theorem: Invariance under Quantum Permutations is Equivalent to Freeness with Amalgamation
Köstler, Claus; Speicher, Roland
We showthat the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen 'exchangeability' (i.e., invariance of the joint distribution of the random variables under the action of the permutation group) to invariance under the action of the quantum permutation group. More precisely, for an infinite sequence of noncommutative random variables (xi )i?N, we prove that invariance of the joint distribution of the xi's under quantum permutations is equivalent to the fact that the xi 's are identically distributed and free with respect to the conditional expectation onto the tail algebra of the xi 's.
2009-12-31T00:00:00ZOptimal Quantum Feedback Control for Canonical ObservablesGough, John E.http://hdl.handle.net/2160/420272016-04-13T22:09:22Z2008-11-12T00:00:00ZOptimal Quantum Feedback Control for Canonical Observables
Gough, John E.
We consider the problem of optimal feedback control of a quantum system with linear dynamics undergoing continual non-demolition measurement of position and/or momentum, or both together. Specically, we show that a stable domain of solutions for the ltered state of the system will be given by a class of randomized squeezed states and we exercise the control problem amonst these states. Bellman's principle is then applied directly to optimal feedback control of such dynamical systems and the Hamilton Jacobi Bellman equation for the minimum cost is derived. The situation of quadratic performance criteria is treated as the important special case and solved exactly for the class of relaxed states.
John Gough, in Quantum Stochastics and Information: Statistics, Filtering & Control, pp. 262-279 Eds. M. Guta and V.P. Belavkin, World Scientific 2008 ISBN#: 9789812832955
2008-11-12T00:00:00ZSymmetry and Independence in Quantum ProbabilityKoestler, Claushttp://hdl.handle.net/2160/404662016-04-13T23:11:16Z2010-12-08T00:00:00ZSymmetry and Independence in Quantum Probability
Koestler, Claus
numberexhibits: 1
2010-12-08T00:00:00ZSingle Photon Quantum Filtering Using non-Markov EmbeddingsGough, John EdwardJames, Matthew R.Nurdin, Hendra I.http://hdl.handle.net/2160/346402016-03-24T15:25:59Z2012-11-28T00:00:00ZSingle Photon Quantum Filtering Using non-Markov Embeddings
Gough, John Edward; James, Matthew R.; Nurdin, Hendra I.
We determine quantum master and filter equations for continuous measurement of systems coupled to input fields in certain non-classical continuous-mode states, specifically single photon states. The quantum filters are shown to be derivable from an embedding into a larger non-Markovian system, and are given by a system of coupled stochastic differential equations.
Gough, J. E., James, M. R., Nurdin, H. I. (2012). Single Photon Quantum Filtering Using non-Markov Embeddings. Philosophical Transactions of The Royal Society A Mathematical, Physical & Engineering Sciences, 370 (1979), 5241-5258.
2012-11-28T00:00:00Z