Decoherence transforms a ballistic quantum walk into a diffusive classical random walk. After each step the environment measures the particle's path and the outside world gets to know the which-way information. The relation between the which-way information and the classicality of the spatial distribution is clearly visible in the multi-coin quantum walk in which the information about particle's path is encoded in the multi-coin degree of freedom. The more information is stored on the coins, the more classical and diffusive the spatial distribution is. Here, we propose a generalized version of the quantum eraser scenario that allows for complex erasure strategies. We show that the which-way information can be erased from the coins and the ballistic features in the spatial probability distribution can be recovered.Decoherence transforms a ballistic quantum walk into a diffusive classical random walk. After each step the environment measures the particle's path and the outside world gets to know the which-way information. The relation between the which-way information and the classicality of the spatial distribution is clearly visible in the multi-coin quantum walk in which the information about particle's path is encoded in the multi-coin degree of freedom. The more information is stored on the coins, the more classical and diffusive the spatial distribution is. Here, we propose a generalized version of the quantum eraser scenario that allows for complex erasure strategies. We show that the which-way information can be erased from the coins and the ballistic features in the spatial probability distribution can be recovered.

arXiv:1812.00624Dec 3, 20180 citations

Homogeneous Open Quantum Random Walks on a Lattice

Raffaella Carbone, Yan Pautrat

arXiv:1408.1113Journal of Statistical PhysicsMay 25, 201541 citations

Generic quantum walk using a coin-embedded shift operator

C. M. Chandrashekar

The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by considering the limiting value of the coin operation parameter in the DTQW, and the coin degree of freedom was shown to be unnecessary [F. W. Strauch, Phys. Rev. A 74, 030301(R) (2006)]. But the coin degree of freedom is an additional resource which can be exploited to control the dynamics of the QW process. In this paper we present a generic quantum walk model using a quantum coin-embedded unitary shift operation ${U}_{C}$ . The standard version of the DTQW and the CTQW can be conveniently retrieved from this generic model, retaining the features of the coin degree of freedom in both variants.The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by considering the limiting value of the coin operation parameter in the DTQW, and the coin degree of freedom was shown to be unnecessary [F. W. Strauch, Phys. Rev. A 74, 030301(R) (2006)]. But the coin degree of freedom is an additional resource which can be exploited to control the dynamics of the QW process. In this paper we present a generic quantum walk model using a quantum coin-embedded unitary shift operation ${U}_{C}$. The standard version of the DTQW and the CTQW can be conveniently retrieved from this generic model, retaining the features of the coin degree of freedom in both variants.

arXiv:0810.1556Physical Review ANov 5, 200810 citations

Homogeneous open quantum walks on the line: criteria for site recurrence and absorption

Thomas S. Jacq, Carlos F. Lardizabal

In this work, we study open quantum random walks, as described by S. Attal et al.. These objects are given in terms of completely positive maps acting on trace-class operators, leading to one of the simplest open quantum versions of the recurrence problem for classical, discrete-time random walks. This work focuses on obtaining criteria for site recurrence of nearest-neighbor, homogeneous walks on the integer line, with the description presented here making use of recent results of the theory of open walks, most particularly regarding reducibility properties of the operators involved. This allows us to obtain a complete criterion for site recurrence in the case for which the internal degree of freedom of each site (coin space) is of dimension 2. We also present the analogous result for irreducible walks with an internal degree of arbitrary finite dimension and the absorption problem for walks on the semi-infinite line.In this work, we study open quantum random walks, as described by S. Attal et al.. These objects are given in terms of completely positive maps acting on trace-class operators, leading to one of the simplest open quantum versions of the recurrence problem for classical, discrete-time random walks. This work focuses on obtaining criteria for site recurrence of nearest-neighbor, homogeneous walks on the integer line, with the description presented here making use of recent results of the theory of open walks, most particularly regarding reducibility properties of the operators involved. This allows us to obtain a complete criterion for site recurrence in the case for which the internal degree of freedom of each site (coin space) is of dimension 2. We also present the analogous result for irreducible walks with an internal degree of arbitrary finite dimension and the absorption problem for walks on the semi-infinite line.

arXiv:2010.03085Quantum Information and ComputationFeb 1, 20216 citations

Quantum Markov Chains Associated with Open Quantum Random Walks

Ameur Dhahri, Chul Ki Ko, Hyun Jae Yoo

arXiv:1808.03479Journal of Statistical PhysicsJun 21, 201923 citations

{U}_{C}

. The standard version of the DTQW and the CTQW can be conveniently retrieved from this generic model, retaining the features of the coin degree of freedom in both variants.