Quantum walker as a probe for its coin parameter
arXiv:1901.00614 · doi:10.1103/PhysRevA.99.052117
Abstract
In discrete-time quantum walk (DTQW) the walker's coin space entangles with the position space after the very first step of the evolution. This phenomenon may be exploited to obtain the value of the coin parameter by performing measurements on the sole position space of the walker. In this paper, we evaluate the ultimate quantum limits to precision for this class of estimation protocols, and use this result to assess measurement schemes having limited access to the position space of the walker in one dimension. We find that the quantum Fisher information (QFI) of the walker's position space increases with and with time which, in turn, may be seen as a metrological resource. We also find a difference in the QFI of {\em bounded} and {\em unbounded} DTQWs, and provide an interpretation of the different behaviors in terms of interference in the position space. Finally, we compare to the full QFI , i.e., the QFI of the walkers position plus coin state, and find that their ratio is dependent on , but saturates to a constant value, meaning that the walker may probe its coin parameter quite faithfully.
10 Pages, 11 figures, published version
References in corpus (51)
- Quantum random walks - an introductory overview
- Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
- Universal computation by quantum walk
- Quantum walks of correlated particles
- Quantum walks: a comprehensive review
- Exponential algorithmic speedup by quantum walk
- Spatial search by quantum walk
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Observation of topologically protected bound states in a one dimensional photonic system
- Photons Walking the Line: A quantum walk with adjustable coin operations
- Exploring Topological Phases With Quantum Walks
- From quantum cellular automata to quantum lattice gases
- Realization of quantum walks with negligible decoherence in waveguide lattices
- Realization of a quantum walk with one and two trapped ions
- Quantum walk of a trapped ion in phase space
- Discrete single-photon quantum walks with tunable decoherence
- Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
- Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
- Asymptotic evolution of quantum walks with random coin
- Optimizing the discrete time quantum walk using a SU(2) coin
- Recurrence and Pólya number of quantum walks
- Topological phases and delocalization of quantum walks in random environments
- Relationship Between Quantum Walk and Relativistic Quantum Mechanics
- Relativistic quantum walks
- Classical approach to the graph isomorphism problem using quantum walks
- Quantum Walks in artificial electric and gravitational Fields
- Quantum probes for the spectral properties of a classical environment
- Quantum probes for the cutoff frequency of Ohmic environments
- Characterization of classical Gaussian processes using quantum probes
- Quantum Walks as simulators of neutrino oscillations in vacuum and matter
- Scattering theory of topological phases in discrete-time quantum walks
- Entangled quantum probes for dynamical environmental noise
- Continuous-variable quantum probes for structured environments
- Two-component Dirac-like Hamiltonian for generating quantum walk on one-, two- and three-dimensional lattices
- Asymptotic dynamics of coined quantum walks on percolation graphs
- Quantum walks as massless Dirac Fermions in curved Space-Time
- Characterization of qubit chains by Feynman probes
- Quantum percolation and transition point of a directed discrete-time quantum walk
- Dirac Quantum Cellular Automaton from Split-step Quantum Walk
- Neutrino oscillations in discrete-time quantum walk framework
- Quantum probes to assess correlations in a composite system
- Localized quantum walks as secured quantum memory
- Universal quantum magnetometry with spin states at equilibrium
- Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation
- Quantum probes for fractional Gaussian processes
- Disorder induced localization and enhancement of entanglement in one- and two-dimensional quantum walks
- Can quantum probes satisfy the weak equivalence principle?
- Decomposition of split-step quantum walks for simulating Majorana modes and edge states
- Asymptotic properties of the Dirac quantum cellular automaton
- Fractional recurrence in discrete-time quantum walk
- Probing the sign of on-site Hubbard interaction by two-particle quantum walks
Cited by in corpus (5)
- Multi-parameter quantum metrology with discrete-time quantum walks
- Quantum magnetometry using discrete-time quantum walk
- Coin dimensionality as a resource in quantum metrology involving discrete-time quantum walks
- Improving quantum walk metrology with split-step quantum walk
- Optimizing topology for quantum probing with discrete-time quantum walks