A Correlated Quantum Walk

Eman Hamza, Alain Joye

Franklin de Lima Marquezino, Renato Portugal, Carlile Lavor

Jin-Fu Chen, Yu-Han Ma, Chang-Pu Sun

Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation between different steps in QW and leads to a non-binomial position distribution. In this paper, we propose an alternative quantum extension of CRW from the ensemble interpretation, named quantum random walk (QRW), where the walker has many unrelated coins, modeled as two-level systems, initially prepared in the same state. We calculate the walker’s position distribution in QRW for different initial coin states with the coin operator chosen as Hadamard matrix. In one-dimensional case, the walker’s position is the asymmetric binomial distribution. We further demonstrate that in QRW, coherence leads the walker to perform directional movement. For an initially decoherenced coin state, the walker’s position distribution is exactly the same as that of CRW. Moreover, we study QRW in 2D lattice, where the coherence plays a more diversified role in the walker’s position distribution.

Norio Konno

Alessandro Laneve, Farzam Nosrati, Andrea Geraldi +5 more

The presence of disorder and inhomogeneities in quantum networks has often been unexpectedly beneficial for both quantum and classical resources. Here we experimentally realize a controllable inhomogenous quantum walk (QW) dynamics, which can be exploited to investigate the effect of coherent disorder on the quantum correlations between two indistinguishable photons. Through the imposition of suitable disorder configurations, we observe two-photon states that exhibit an enhancement in the quantum correlations between two selected modes of the network, compared to the case of an ordered QW. Different configurations of disorder can steer the system toward different realizations of such an enhancement, thus allowing spatial and temporal manipulation of quantum correlations between remote modes of QW networks.

Simon Moulieras, Maciej Lewenstein, Graciana Puentes

Discrete-time quantum walks (QWs) represent robust and versatile platforms for the controlled engineering of single particle quantum dynamics, and have attracted special attention due to their algorithmic applications in quantum information science. Even in their simplest 1D architectures, they display complex topological phenomena, which can be employed in the systematic study of topological quantum phase transitions [1]. Due to the exponential scaling in the number of resources required, most experimental realizations of QWs to date have been limited to single particles, with only a few implementations involving correlated quantum pairs. In this paper we study applications of QWs in the controlled dynamical engineering of entanglement in bipartite bosonic systems. We show that QWs can be employed in the transition from mode entanglement, where indistinguishability of the quantum particles plays a key role, to the standard type of entanglement associated with distinguishable particles. We also show that by carefully tailoring the steps in the QWs, as well as the initial state for the quantum walker, it is possible to preserve the entanglement content by topological protection. The underlying mechanism that allows for the possibility of both entanglement engineering and entanglement protection is the strong ‘spin–orbit’ coupling induced by the QW. We anticipate that the results reported here can be employed for the controlled emulation of quantum correlations in topological phases.