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Asymptotic distributions of quantum walks on the line with two entangled coins

Chaobin Liu

arXiv:1107.3346Quantum Information ProcessingJan 25, 201222 citations

Quantum walk with a general coin: exact solution and asymptotic properties

Miquel Montero

arXiv:1310.7486Quantum Information ProcessingJan 6, 201510 citations

Time exponents of asymptotic entanglement of discrete quantum walk in one dimension

Recep Eryiğit, Semra Gündüç

We report a systematic study of asymptotic behavior of entanglement between the position and coin degrees of freedom for a one-dimensional discrete quantum walk. Effects of coin bias, initial coin asymmetry and phase difference and non-locality of initial position state on the fluctuations and asymptotic value of entanglement are investigated by using Fourier approach. Fluctuations in entropy are found to die out as power law in time as t-α with α = 1/2,3/2 and 5/2 depending on the initial state parameters of the system.We report a systematic study of asymptotic behavior of entanglement between the position and coin degrees of freedom for a one-dimensional discrete quantum walk. Effects of coin bias, initial coin asymmetry and phase difference and non-locality of initial position state on the fluctuations and asymptotic value of entanglement are investigated by using Fourier approach. Fluctuations in entropy are found to die out as power law in time as t-α with α = 1/2,3/2 and 5/2 depending on the initial state parameters of the system.

International Journal of Quantum InformationSep 1, 20145 citations

Asymptotic behavior of quantum walks on the line

Toshikazu Sunada, Tatsuya Tate

arXiv:1108.1878Journal of Functional AnalysisJan 25, 201242 citations

Discrete-Time Quantum Walks with Even-Dimensional Coins

Yunguo Lin, Yong Wang, Chengwei Zheng +3 more

Jan 1, 20260 citations

Asymptotic reduced density matrix of discrete-time quantum walks

Mostafa Annabestani

Abstract In this article we show that for any quantum walker with m -dimensional coin subspace, we have m 2 × m 2 specific constant matrix C where it completely determines the asymptotic reduced density matrix of the walker. We show that for any initial state with P 0 projector, the reduced density matrix can be obtained by T r 1 P 0 ⊗ I C or equivalently T r 2 I ⊗ P 0 C . It is worth mentioning that the characteristic matrix C is independent of the initial state and just depends on the coin operator, so by finding this matrix for a specific type of quantum walks (QW), the long-time behavior of it, such as local state of the coin after a long-time walk and asymptotic entanglement between the coin and position will be completely known for any initial state. We have found the characteristic matrix C for the general coin operator, U 2 , as well as the exact form of this matrix for the local initial state.Abstract In this article we show that for any quantum walker with m -dimensional coin subspace, we have m 2 × m 2 specific constant matrix C where it completely determines the asymptotic reduced density matrix of the walker. We show that for any initial state with P 0 projector, the reduced density matrix can be obtained by T r 1 P 0 ⊗ I C or equivalently T r 2 I ⊗ P 0 C . It is worth mentioning that the characteristic matrix C is independent of the initial state and just depends on the coin operator, so by finding this matrix for a specific type of quantum walks (QW), the long-time behavior of it, such as local state of the coin after a long-time walk and asymptotic entanglement between the coin and position will be completely known for any initial state. We have found the characteristic matrix C for the general coin operator, U 2 , as well as the exact form of this matrix for the local initial state.

arXiv:1909.09214Journal of Physics A Mathematical and TheoreticalFeb 28, 20200 citations

Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations

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