Generalized Intelligent States (coherent and squeezed states) are derived for an arbitrary quantum system by using the minimization of the so-called Robertson-Schrödinger uncertainty relation. The Fock-Bargmann representation is also considered. As a direct illustration of our construction, the Pöschl-Teller potentials of trigonometric type will be shosen. We will show the advantage of the Fock-Bargmann representation in obtaining the generalized intelligent states in an analytical way. Many properties of these states are studied.
This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system $[ 1] $. We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau-Klauder and those à la Klauder-Perelomov, we derive the generalized intelligent states in analytical ways.
The construction of Generalized Intelligent States (GIS) for the $x^4$% -anharmonic oscillator is presented. These GIS families are required to minimize the Robertson-Schrödinger uncertainty relation. As a particular case, we will get the so-called Gazeau-Klauder coherent states. The properties of the latters are discussed in detail. Analytical representation is also considered and its advantage is shown in obtaining the GIS in an analytical way. Further extensions are finally proposed.
Ordinary intelligent states (OIS) hold equality in the Heisenberg uncertainty relation involving two noncommuting observables {A, B}, whereas generalized intelligent states (GIS) do so in the more generalized uncertainty relation, the Schrodinger-Robertson inequality. In general, OISs form a subset of GISs. However, if there exists a unitary evolution U that transforms the operators {A, B} to a new pair of operators in a rotation form, it is shown that an arbitrary GIS can be generated by applying the rotation operator U to a certain OIS. In this sense, the set of OISs is unitarily equivalent …
A sufficient condition for a state |ψ> to minimize the Robertson-Schrödinger uncertainty relation for two observables A and B is obtained which for A with no discrete spectrum is also a necessary one. Such states, called generalized intelligent states (GIS), exhibit arbitrarily strong squeezing (after Eberly) of A and B. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the Bloch CS are subset of SU(2) GIS.
We construct nonlinear coherent states or f-deformed coherent states for a nonpolynomial nonlinear oscillator which can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (Cariñena J F et al, J. Phys. A: Math. Theor. 41, 085301 (2008)). The deformed annihilation and creation operators which are required to construct the nonlinear coherent states in the number basis are obtained from the solution of the Schrödinger equation. Using these operators, we construct generalized intelligent states, nonlinear coherent states, Gazeau-Klauder coherent states…
The quantum states which satisfy the equality in the generalised uncertainty relation are called intelligent states. We prove the existence of intelligent states for the Anandan-Aharonov uncertainty relation based on the geometry of the quantum state space for arbitrary parametric evolutions of quantum states when the initial and final states are non-orthogonal.
The Robertson -- Schrödinger, Heisenberg -- Robertson and Trifonov uncertainty relations for arbitrary two functions $f_{1}$ and $f_{2}$ depending on the quantum phase and the number of photons respectively, are given. Intelligent states and states which minimize locally the product of uncertainties $(Δf_{1})^{2}\cdot (Δf_{2})^{2}$ or the sum $(Δf_{1})^{2}+(Δf_{2})^{2}$ are investigated for the cases $f_{1}=ϕ,\exp{(iϕ)}, \exp{(-iϕ)}, \cosϕ, \sinϕ$ and $f_{2}=n$.
We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states associated with a dynamical symmetry group. On the one hand, algebra eigenstates include different sets of Perelomov's generalized coherent states. On the other hand, intelligent states (which are squeezed states for a system of general symmetry) also form a subset of algebra eigenstates. We develop the general formalism and apply it to the SU(2) and SU(1,1) si…
A generalization of the quantum XOR-gate is presented which operates in arbitrary dimensional Hilbert spaces. Together with one-particle Fourier transforms this gate is capable of performing a variety of tasks which are important for quantum information processing in arbitrary dimensional Hilbert spaces. Among these tasks are the preparation of Bell states, quantum teleportation and quantum state purification. A physical realization of this generalized XOR-gate is proposed which is based on non-linear optical elements.
Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems with a known discrete spectrum as well as the generalized coherent states with known nonlinearity function $f (n)$. As some physical appearance of the proposed formalism, a few new classes of intelligent states associated with \textit{`center of-mass motion of a trapped ion'}, \textit{`harmonious states'} and \textit{`hydrogen-like spectrum'} have been realized…
We propose a generalized structure of Bell inequalities for arbitrary d-dimensional bipartite systems, which includes the existing two types of Bell inequalities introduced by Collins-Gisin-Linden-Massar-Popescu [Phys. Rev. Lett. 88, 040404 (2002)] and Son-Lee-Kim [Phys. Rev. Lett. 96, 060406 (2006)]. We analyze Bell inequalities in terms of correlation functions and joint probabilities, and show that the coefficients of correlation functions and those of joint probabilities are in Fourier transform relations. We finally show that the coefficients in the generalized structure determine the cha…
Positive operator valued measurements on a finite number of N identically prepared systems of arbitrary spin J are discussed. Pure states are characterized in terms of Bloch-like vectors restricted by a SU(2 J+1) covariant constraint. This representation allows for a simple description of the equations to be fulfilled by optimal measurements. We explicitly find the minimal POVM for the N=2 case, a rigorous bound for N=3 and set up the analysis for arbitrary N.
Herein, we present a feasible, general protocol for quantum communication within a network via generalized remote preparation of an arbitrary $m$-qubit entangled state designed with genuine tripartite Greenberger--Horne--Zeilinger-type entangled resources. During the implementations, we construct novel collective unitary operations; these operations are tasked with performing the necessary phase transfers during remote state preparations. We have distilled our implementation methods into a five-step procedure, which can be used to faithfully recover the desired state during transfer. Compared …
Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms. Here we provide a formal resource-theoretic approach for generalized contextuality based on a physically motivated set of free operations with an explicit parametrisation. Then, using an efficient linear programming characterization for the contextual set of prepared-and-measured statistics, we adapt known resource quantifiers for contextuality and nonlocali…
Grover's algorithm for quantum searching of a database is generalized to deal with arbitrary initial amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the r marked and N-r unmarked states. These equations are solved exactly. An expression for the optimal measurement time T \sim O(\sqrt{N/r}) is derived which is shown to depend only on the initial average amplitudes of the marked and unmarked states. A bound on the probability of measuring a marked state is derived, which depends only on the standard deviation of the initial a…
A generalized universal quantum cloning machine is proposed which allows the input to be arbitrary states in symmetric subspace. And it reduces to the universal quantum cloning machine (UQCM) if the input are identical pure states. The generalized cloner is optimal in the sense we compare the input and output reduced density operators at a single qubit. The result for qubits is extended to arbitrary-dimensional states.
Recursive perturbation approach to time-convolutionless master equations: Explicit construction of generalized Lindblad generators for arbitrary open systems
Università degli Studi di Milano（米兰大学）；INFN, Sezione di Milano（意大利国家核物理研究所米兰分部）；University of Freiburg（弗赖堡大学）；Universität Siegen（锡根大学）；Universitat Autònoma de Barcelona（巴塞罗那自治大学）
Multipartite nonlocality in a network is conceptually different from standard multipartite Bell nonlocality. In recent times, network nonlocality has been studied for various topologies. We consider a linear-chain topology of the network and demonstrate the quantum nonlocality (the non-$n$-locality). Such a network scenario involves $n$ number of independent sources and $n+1$ parties, two edge parties (Alice and Charlie), and $n-1$ central parties (Bobs). It is commonly assumed that each party receives only two inputs. In this work, we consider a generalized scenario where the edge parties rec…
Computing entanglement of an arbitrary bipartite or multipartite mixed state is in general not an easy task as it usually involves complex optimization. Here we show that exploiting symmetries of certain mixed states, we can compute a genuine multiparty entanglement measure, the generalized geometric measure for these classes of mixed states. The chosen states have different ranks and consist of an arbitrary number of parties.
We present a general decomposition of the Generalized Toffoli, and for completeness, the multi-target gate using an arbitrary number of clean or dirty ancilla. While prior work has shown how to decompose the Generalized Toffoli using 0, 1, or $O(n)$ many clean ancilla and 0, 1, and $n-2$ dirty ancilla, we provide a generalized algorithm to bridge the gap, i.e. this work gives an algorithm to generate a decomposition for any number of clean or dirty ancilla. While it is hard to guarantee optimality, our decompositions guarantee a decrease in circuit depth as the number of ancilla increases.
Robust Quantum Controllers: Quantum Information -- Thermodynamic Hidden Force Control in Intelligent Robotics based on Quantum Soft Computing
Institute of System Analysis and Management, Dubna State University（杜布纳国立大学系统分析与管理研究所）；Joint Institute for Nuclear Research (JINR)（联合核子研究所）；Moscow State University of Geodesy and Cartography (MIIGAiK)（莫斯科测绘大学）；Yamaha Motor Co. Ltd.（雅马哈发动机株式会社）
The bound state solution of the radial Schrödinger equation with the generalized Woods-Saxon potential is carefully examined by using the Pekeris approximation for arbitrary $\ell$ states. The energy eigenvalues and the corresponding eigenfunctions are analytically obtained for different $n$ and $\ell$ quantum numbers. The obtained closed forms are applied to calculate the single particle energy levels of neutron orbiting around $^{56}$Fe nucleus in order to check consistency between the analytical and Gamow code results. The analytical results are in good agreement with the results obtained b…
Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it $Ω$ (the $S^{d-1}-$ sphere, in our case). We shall show how particles arrange themselves under the sole action of the Coulomb repulsion in many dimensions in the usual Euclidean space, therefore generalizing the so called Thomson problem to many dimensions. Also, we explore how the problem varies when non-Euclidean geometries are considered. We shall see that optimal configurations in all cases possess…
Boundary conditions for the Maxwell and Dirac fields at material surfaces are widely-used and physically well-motivated, but do not appear to have been generalised to deal with higher spin fields. As a result there is no clear prescription as to which boundary conditions should be selected in order to obtain physically-relevant results pertaining to confined higher spin fields. This lack of understanding is significant given that boundary-dependent phenomena are ubiquitous across physics, a prominent example being the Casimir effect. Here, we use the two-spinor calculus formalism to present a …
We study the spontaneous de-excitation and excitation of accelerated atoms on arbitrary stationary trajectories (``generalized Unruh effect''). We consider the effects of vacuum fluctuations and radiation reaction separately. We show that radiation reaction is generally not altered by stationary acceleration, whereas the contribution of vacuum fluctuations differs for all stationary accelerated trajectories from its inertial value. Spontaneous excitation from the ground state occurs for all { accelerated stationary} trajectories and is therefore the ``normal case''. We furthermore show that th…
It is found that identical bosons (fermions) show generalized bunching (antibunching) property in linear networks: The absolute maximum (minimum) of probability that all $N$ input particles are detected in a subset of $\mathcal{K}$ output modes of any nontrivial linear $M$-mode network is attained \textit{only} by completely indistinguishable bosons (fermions). For fermions $\mathcal{K}$ is arbitrary, for bosons it is either ($i$) arbitrary for only classically correlated bosons or ($ii$) satisfies $\mathcal{K}\ge N$ (or $\mathcal{K}=1$) for arbitrary input states of $N$ particles. The general…
