The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
R. Tiedra De Aldecoa - One of the best experts on this subject based on the ideXlab platform.
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Stationary scattering theory for Unitary Operators with an application to quantum walks
Journal of Functional Analysis, 2020Co-Authors: R. Tiedra De AldecoaAbstract:Abstract We present a general account on the stationary scattering theory for Unitary Operators in a two-Hilbert spaces setting. For Unitary Operators U 0 , U in Hilbert spaces H 0 , H and an identification operator J : H 0 → H , we give the definitions and collect properties of the stationary wave Operators, the strong wave Operators, the scattering operator and the scattering matrix for the triple ( U , U 0 , J ) . In particular, we exhibit conditions under which the stationary wave Operators and the strong wave Operators exist and coincide, and we derive representation formulas for the stationary wave Operators and the scattering matrix. As an application, we show that these representation formulas are satisfied for a class of anisotropic quantum walks recently introduced in the literature.
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Quantum time delay for Unitary Operators: General theory
Reviews in Mathematical Physics, 2019Co-Authors: D. Sambou, R. Tiedra De AldecoaAbstract:We present a suitable framework for the definition of quantum time delay in terms of sojourn times for Unitary Operators in a two-Hilbert spaces setting. We prove that this time delay defined in te...
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Quantum walks with an anisotropic coin II: scattering theory
Letters in Mathematical Physics, 2019Co-Authors: S. Richard, A. Suzuki, R. Tiedra De AldecoaAbstract:We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. Our analysis is based on an abstract framework for the scattering theory of Unitary Operators in a two-Hilbert spaces setting, which is of independent interest.
Xiaoguang Wang - One of the best experts on this subject based on the ideXlab platform.
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matrix realignment and partial transpose approach to entangling power of quantum evolutions
Physical Review A, 2007Co-Authors: Xiaoguang WangAbstract:Based on the matrix realignment and partial transpose, we develop an approach to the entangling power and operator entanglement of quantum Unitary Operators. We demonstrate the approach by studying several Unitary Operators on qudits, and indicate that these two matrix rearrangements are convenient to use in studying entangling capabilities of quantum Operators.
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quantum entanglement of Unitary Operators on bipartite systems
Physical Review A, 2002Co-Authors: Xiaoguang Wang, Paolo ZanardiAbstract:We study the entanglement of Unitary Operators on ${d}_{1}\ifmmode\times\else\texttimes\fi{}{d}_{2}$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of Unitary Operators is quantified by the concept of concurrence.
Soonchil Lee - One of the best experts on this subject based on the ideXlab platform.
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storing Unitary Operators in quantum states
Physical Review A, 2001Co-Authors: Jaehyun Kim, Jae-seung Lee, Yongwook Cheong, Soonchil LeeAbstract:We present a scheme to store Unitary Operators with self-inverse generators in quantum states and a general circuit to retrieve them with definite success probability. The continuous variable of the operator is stored in a single-qubit state and the information about the kind of the operator is stored in classical states with finite dimension. The probability of successful retrieval is always 1/2 irrespective of the kind of the operator, which is proved to be maximum. In case of failure, the result can be corrected with additional quantum states. The retrieving circuit is almost as simple as that which handles only the single-qubit rotations and CNOT as the basic operations. An interactive way to transfer quantum dynamics, that is, to distribute naturally copy-protected programs for quantum computers is also presented using this scheme.
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Implementing Unitary Operators in quantum computation
Physical Review A, 2000Co-Authors: Jaehyun Kim, Jae-seung Lee, Soonchil LeeAbstract:We present a general method which expresses a Unitary operator by the product of Operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by the base Operators of the product operator formalism. Finally, the base Operators disallowed by the Hamiltonian, including more than two-body interaction Operators, are replaced by allowed ones by the axes transformation and coupling order reduction technique. This method directly provides pulse sequences for the nuclear magnetic resonance quantum computer, and can be generally applied to other systems.
Arun Kumar Pati - One of the best experts on this subject based on the ideXlab platform.
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experimental test of uncertainty relations for general Unitary Operators
Optics Express, 2017Co-Authors: Lei Xiao, Kunkun Wang, Xiang Zhan, Zhihao Bian, Jian Li, Yongsheng Zhang, Arun Kumar PatiAbstract:Uncertainty relations are the hallmarks of quantum physics and have been widely investigated since its original formulation. To understand and quantitatively capture the essence of preparation uncertainty in quantum interference, the uncertainty relations for Unitary Operators need to be investigated. Here, we report the first experimental investigation of the uncertainty relations for general Unitary Operators. In particular, we experimentally demonstrate the uncertainty relation for general Unitary Operators proved by Bagchi and Pati [ Phys. Rev. A94, 042104 (2016)], which places a non-trivial lower bound on the sum of uncertainties and removes the triviality problem faced by the product of the uncertainties. The experimental findings agree with the predictions of quantum theory and respect the new uncertainty relation.
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Uncertainty relations for general Unitary Operators
Physical Review A, 2016Co-Authors: Shrobona Bagchi, Arun Kumar PatiAbstract:We derive several uncertainty relations for two arbitrary Unitary Operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the uncertainty relation for the Unitary Operators, we obtain the tight state-independent lower bound for the uncertainty of two Pauli observables and anticommuting observables in higher dimensions. With regard to the minimum-uncertainty states, we derive the minimum-uncertainty state equation by the analytic method and relate this to the ground-state problem of the Harper Hamiltonian. Furthermore, the higher-dimensional limit of the uncertainty relations and minimum-uncertainty states are explored. From an operational point of view, we show that the uncertainty in the Unitary operator is directly related to the visibility of quantum interference in an interferometer where one arm of the interferometer is affected by a Unitary operator. This shows a principle of preparation uncertainty, i.e., for any quantum system, the amount of visibility for two general noncommuting Unitary Operators is nontrivially upper bounded.
V H Cortes - One of the best experts on this subject based on the ideXlab platform.
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commutation relations for Unitary Operators ii
Journal of Approximation Theory, 2015Co-Authors: M A Astaburuaga, Olivier Bourget, V H CortesAbstract:Let f be a regular non-constant symbol defined on the d -dimensional torus T d with values on the unit circle. Denote respectively by ? and L , its set of critical points and the associated Laurent operator on l 2 ( Z d ) . Let U be a suitable Unitary local perturbation of L . We show that the operator U has finite point spectrum and no singular continuous component away from the set f ( ? ) . We apply these results and provide a new approach to analyze the spectral properties of GGT matrices with asymptotically constant Verblunsky coefficients. The proofs are based on positive commutator techniques. We also obtain some propagation estimates.
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commutation relations for Unitary Operators i
Journal of Functional Analysis, 2015Co-Authors: M A Astaburuaga, Olivier Bourget, V H CortesAbstract:Abstract Let U be a Unitary operator defined on some infinite-dimensional complex Hilbert space H . Under some suitable regularity assumptions, it is known that a positive commutation relation between U and an auxiliary self-adjoint operator A defined on H allows to prove that the spectrum of U has locally no singular continuous spectrum and a finite point spectrum. We show that these conclusions still hold under weak regularity hypotheses and without any gap condition. As an application, we study the spectral properties of the Floquet operator associated to some perturbations of the quantum harmonic oscillator under resonant AC-Stark potential.
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commutation relations for Unitary Operators ii
arXiv: Functional Analysis, 2013Co-Authors: M A Astaburuaga, Olivier Bourget, V H CortesAbstract:Let $U$ be a Unitary operator defined on some infinite-dimensional complex Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is known that a local positive commutation relation between $U$ and an auxiliary self-adjoint operator $A$ defined on ${\cal H}$ allows to prove that the spectrum of $U$ has no singular continuous spectrum and a finite point spectrum, at least locally. We prove that under stronger regularity hypotheses, the local regularity properties of the spectral measure of $U$ are improved, leading to a better control of the decay of the correlation functions. As shown in the applications, these results may be applied to the study of periodic time-dependent quantum systems, classical dynamical systems and spectral problems related to the theory of orthogonal polynomials on the unit circle.
