Hidden Quantum Markov Models and non-adaptive read-out of many-body states
| Autor: | Monras, Alex, Beige, Almut, Wiesner, Karoline |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Applied Mathematical and Computational Sciences 3, 93 (2011) |
| Druh dokumentu: | Working Paper |
| Popis: | Stochastic finite-state generators are compressed descriptions of infinite time series. Alternatively, compressed descriptions are given by quantum finite- state generators [K. Wiesner and J. P. Crutchfield, Physica D 237, 1173 (2008)]. These are based on repeated von Neumann measurements on a quantum dynamical system. Here we generalise the quantum finite-state generators by replacing the von Neumann pro jections by stochastic quantum operations. In this way we assure that any time series with a stochastic compressed description has a compressed quantum description. Moreover, we establish a link between our stochastic generators and the sequential readout of many-body states with translationally-invariant matrix product state representations. As an example, we consider the non-adaptive read-out of 1D cluster states. This is shown to be equivalent to a Hidden Quantum Model with two internal states, providing insight on the inherent complexity of the process. Finally, it is proven by example that the quantum description can have a higher degree of compression than the classical stochastic one. Comment: 22 pages, 5 figures |
| Databáze: | arXiv |
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