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GR Grimmett, DR Stirzaker (2001)
Probability and Random Processes
S. Attal, Francesco Petruccione, C. Sabot, I. Sinayskiy (2012)
Open Quantum Random WalksJournal of Statistical Physics, 147
P. Sinkovicz, Tamás Kiss, J. Asbóth (2015)
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J Bourgain, FA Grünbaum, L Velázquez, J Wilkening (2014)
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K. Vogler (2016)
Table Of Integrals Series And Products
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Inequalities: Majorization and its Applications
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Limit Theorems for Open Quantum Random WalksJournal of Statistical Physics, 150
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Quantum Walks and Search Algorithms
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Central limit theorem for reducible and irreducible open quantum walksQuantum Information Processing, 15
D. Petz (2007)
Quantum Information Theory and Quantum Statistics
S. Attal, N. Guillotin-Plantard, C. Sabot (2012)
Central Limit Theorems for Open Quantum Random Walks and Quantum Measurement RecordsAnnales Henri Poincaré, 16
J. Bourgain, F. Grünbaum, L. Velázquez, J. Wilkening
Communications in Mathematical Physics Quantum Recurrence of a Subspace and Operator-Valued Schur Functions
R. Carbone, Y. Pautrat (2014)
Open Quantum Random Walks: Reducibility, Period, Ergodic PropertiesAnnales Henri Poincaré, 17
Sheng Xiong, Wei-Shih Yang (2013)
Open Quantum Random Walks with Decoherence on Coins with n Degrees of FreedomJournal of Statistical Physics, 152
I. Sinayskiy, Francesco Petruccione (2015)
Microscopic derivation of open quantum Brownian motion: a particular examplePhysica Scripta, T165
R. Carbone, Y. Pautrat (2014)
Homogeneous Open Quantum Random Walks on a LatticeJournal of Statistical Physics, 160
M. Štefaňák, I. Jex, T. Kiss (2007)
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R. Horn, Charles Johnson (1991)
Topics in Matrix Analysis
R Bhatia (2007)
Positive Definite Matrices
C. Lardizabal, Rafael Souza (2015)
Open Quantum Random Walks: Ergodicity, Hitting Times, Gambler’s Ruin and Potential TheoryJournal of Statistical Physics, 164
S. Venegas-Andraca (2012)
Quantum walks: a comprehensive reviewQuantum Information Processing, 11
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Probability and Random Processes, 3rd edn
F. Grünbaum, L. Velázquez, A. Werner, R. Werner (2012)
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C. Lardizabal, Rafael Souza (2014)
On a Class of Quantum Channels, Open Random Walks and RecurrenceJournal of Statistical Physics, 159
We study the problem of site recurrence of discrete-time nearest-neighbor open quantum random walks (OQWs) on the integer line, proving basic properties and some of its relations with the corresponding problem for unitary (coined) quantum walks (UQWs). For both kinds of walks, our discussion concerns two notions of recurrence, one given by a monitoring procedure (Grünbaum et al. in Commun Math Phys 320:543–569, 2013; Lardizabal and Souza in J Stat Phys 159:772–796, 2015), and we study their similarities and differences. In particular, by considering UQWs and OQWs induced by the same pair of matrices, we discuss the fact that recurrence of these walks is related by an additive interference term in a simple way. Based on a previous result of positive recurrence, we describe an open quantum version of Kac’s lemma for the expected return time to a site.
Quantum Information Processing – Springer Journals
Published: Dec 17, 2016
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