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Register a new userQuantum interference and coherence in one-dimensional disordered and localized quantum walk
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One-dimensional discrete-time quantum walk has played an important role in development of quantum algorithms and protocols for different quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum interference and coherence of the wave packet in position space. Similarly, localization in quantum walk due to disorder is also attributed to quantum interference effect. Therefore, it is intriguing to have a closer look and understand the way quantum interference manifests in different forms of quantum walk dynamics. Quantum coherence in the system is responsible for quantum interference in the system. Here we will use coherence measure to quantify the interference in the discrete-time quantum walk. We show coherence in the position and coin space, together and independently, and present the contribution of coherence to the quantum interference in the system. This study helps us to differentiate the localization seen in one dimensional discrete-time quantum walks due to different forms of disorders and topological effects.
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Symmetrically evolving discrete quantum walk results in dynamic localization with zero mean displacement when the standard evolution operations are replaced by a temporal disorder evolution operation. In this work we show that the quantum ratchet action, that is, a directed transport in standard or disordered discrete-time quantum walk can be realized by introducing a pawl like effect realized by using a fixed coin operation at marked positions that is, different from the ones used for evolution at other positions. We also show that the combination of standard and disordered evolution operations can be optimized to get the mean displacement of order $propto$ t (number of walk steps). This model of quantum ratchet in quantum walk is defined using only a set of entangling unitary operators resulting in the coherent quantum transport.
We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We employ Quantum Fisher Information, as a figure of merit, to quantify extractable information about an unknown parameter encoded within the Quantum Walk evolution. Although the approach is universal, we focus on the coherent static and dynamic disorder to investigate anomalous and classical transport as well as Anderson localization. Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks, both classical and quantum.
In this study, we investigate pairwise non-classical correlations measured using a one-way quantum deficit as well as quantum coherence in the $XY$ spin-1/2 chain in a transverse magnetic field for both zero and finite temperatures. The analytical and numerical results of our investigations are presented. In the case when the temperature is zero, it is shown that the one-way quantum deficit can characterize quantum phase transitions as well as quantum coherence. We find that these measures have a clear critical point at $lambda=1$. When $lambdale1$, the one-way quantum deficit has an analytical expression that coincides with the relative entropy of coherence. We also study an $XX$ model and an Ising chain at the finite temperatures.
We investigate coherence in one- and two-photon optical systems, both theoretically and experimentally. In the first case, we develop the density operator representing a single photon state subjected to a non-dissipative coupling between observed (polarization) and unobserved (frequency) degrees of freedom. We show that an implementation of ``bang-bang quantum control protects photon polarization information from certain types of decoherence. In the second case, we investigate the existence of a decoherence-free subspace of the Hilbert space of two-photon polarization states under the action of a similar coupling. The density operator representation is developed analytically and solutions are obtained numerically. NOTE: This manuscript is taken from the authors undergraduate thesis (A.B. Dartmouth College, June 2000, advised by Dr. Walter E. Lawrence), under the supervision of Dr. Paul G. Kwiat.
We study a spin-1/2-particle moving on a one dimensional lattice subject to disorder induced by a random, space-dependent quantum coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the shift operation is assumed to be deterministic. Each coin is an independent identically distributed random variable with values in the group of two dimensional unitary matrices. We derive sufficient conditions on the probability distribution of the coins such that the system exhibits dynamical localization. Put differently, the tunneling probability between two lattice sites decays rapidly for almost all choices of random coins and after arbitrary many time steps with increasing distance. Our findings imply that this effect takes place if the coin is chosen at random from the Haar measure, or some measure continuous with respect to it, but also for a class of discrete probability measures which support consists of two coins, one of them being the Hadamard coin.
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