While two hidden Markov process (HMP) resp. quantum random walk (QRW) parametrizations can differ from one another, the stochastic processes arising from them can be equivalent. Here a polynomial-time algorithm is presented which can determine equivalence of two HMP parametrizations M1, M2resp. two QRW parametrizations Q1, Q2in time O(|Σ| max(N1, N2)4), where N1,N2are the number of hidden states in M1, M2resp. the dimension of the state spaces associated with Q1, Q2, and Σ is the set of output symbols. Previously avail able algorithms for testing equivalence of HMPs were exponential in the number of hidden states. In case of QRWs, algorithms for testing equivalence had not yet been presented. The core subrou tines of this algorithm can also be used to efficiently test hidden Markov processes and quantum random walks for ergodicity.While two hidden Markov process (HMP) resp. quantum random walk (QRW) parametrizations can differ from one another, the stochastic processes arising from them can be equivalent. Here a polynomial-time algorithm is presented which can determine equivalence of two HMP parametrizations M1, M2resp. two QRW parametrizations Q1, Q2in time O(|Σ| max(N1, N2)4), where N1,N2are the number of hidden states in M1, M2resp. the dimension of the state spaces associated with Q1, Q2, and Σ is the set of output symbols. Previously avail able algorithms for testing equivalence of HMPs were exponential in the number of hidden states. In case of QRWs, algorithms for testing equivalence had not yet been presented. The core subrou tines of this algorithm can also be used to efficiently test hidden Markov processes and quantum random walks for ergodicity.

arXiv:0808.2833IEEE Transactions on Information TheoryFeb 18, 201111 citations

Markov Properties and Quantum Experiments

Clark Glymour

Springer eBooksNov 2, 200619 citations

Dephasing of qubits due to an observable stochastic variable

Masashi Ban, Sachiko Kitajima, Fumiaki Shibata

Decoherence of qubits under the influence of random phase fluctuations is studied by means of the stochastic Liouville equation, where the phase fluctuations are characterized by means of the Gauss-Markov process and the two-state-jump Markov process. We investigate how an observation of a stochastic variable during the time evolution influences the decoherence of the qubit system. We examine the decays of distinguishability and entanglement of qubit states. It is shown that the decoherence of qubits can be suppressed by the observation of the stochastic variable. It is also found that the suppression of the decoherence does not depend on the observed value.Decoherence of qubits under the influence of random phase fluctuations is studied by means of the stochastic Liouville equation, where the phase fluctuations are characterized by means of the Gauss-Markov process and the two-state-jump Markov process. We investigate how an observation of a stochastic variable during the time evolution influences the decoherence of the qubit system. We examine the decays of distinguishability and entanglement of qubit states. It is shown that the decoherence of qubits can be suppressed by the observation of the stochastic variable. It is also found that the suppression of the decoherence does not depend on the observed value.

Physical Review AFeb 19, 20133 citations

Experimental test of the modified optical Bloch equations for solids using rotary echoes

T. Muramoto, Arthur G. Szabo

Measurements of optical rotary-echo decay of the ${R}_{1}$ (-1/2),\ensuremath{\sigma} transition of ${\mathrm{Cr}}^{3+}$ in dilute ruby at 2 K are described and compared with predictions of two recent modifications (Gauss-Markov and random-telegraph models) of the optical Bloch equations (OBE's). While the modified OBE approximately describes the free-induction decay behavior both in ${\mathrm{Pr}}^{3+}$ : ${\mathrm{LaF}}_{3}$ and ruby, we show that rotary-echo decay in ruby is instead described by the standard OBE. Various aspects of the spin flip-flop model used in the theories are discussed in regard to ruby, as well as other possible dephasing contributions.Measurements of optical rotary-echo decay of the ${R}_{1}$(-1/2),\ensuremath{\sigma} transition of ${\mathrm{Cr}}^{3+}$ in dilute ruby at 2 K are described and compared with predictions of two recent modifications (Gauss-Markov and random-telegraph models) of the optical Bloch equations (OBE's). While the modified OBE approximately describes the free-induction decay behavior both in ${\mathrm{Pr}}^{3+}$:${\mathrm{LaF}}_{3}$ and ruby, we show that rotary-echo decay in ruby is instead described by the standard OBE. Various aspects of the spin flip-flop model used in the theories are discussed in regard to ruby, as well as other possible dephasing contributions.

Physical Review ADec 1, 198819 citations

Measurements of optical rotary-echo decay of the

{R}_{1}

(-1/2),\ensuremath{\sigma} transition of

{\mathrm{Cr}}^{3+}

in dilute ruby at 2 K are described and compared with predictions of two recent modifications (Gauss-Markov and random-telegraph models) of the optical Bloch equations (OBE's). While the modified OBE approximately describes the free-induction decay behavior both in

{\mathrm{Pr}}^{3+}

{\mathrm{LaF}}_{3}

and ruby, we show that rotary-echo decay in ruby is instead described by the standard OBE. Various aspects of the spin flip-flop model used in the theories are discussed in regard to ruby, as well as other possible dephasing contributions.