Related papers: An algorithm for the optical equivalence theorem
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
We report an algorithm, based on quantum optics formulation, where a coherent state is used as the elementary quantum resource for the image representation. We provide an architecture with constituent optical elements in linear order with…
This paper addresses a construction of new $q-$Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three-term recursive relation as well as the second-order…
We use the spatial degree of freedom of light modes to construct optical analogues of generalized quantum coherent states for Hermite- and Laguerre-Gauss modes. Our optical analogues preserve the statistical properties of their quantum…
Using coherent states in optical quantum process tomography is a practically-relevant approach. Here, we develop a framework for complete characterization of quantum-optical processes in terms of normally-ordered moments by using coherent…
We present a variation of the modular algorithm for computing the Hermite Normal Form of an $\OK$-module presented by Cohen, where $\OK$ is the ring of integers of a number field K. The modular strategy was conjectured to run in polynomial…
Explicit expressions for optical tomograms of the photon-added coherent states, even/odd photon-added coherent states and photon-added thermal states are given in terms of Hermite polynomials. Suggestions for experimental homodyne detection…
Given a square, nonsingular matrix of univariate polynomials $\mathbf{F} \in \mathbb{K}[x]^{n \times n}$ over a field $\mathbb{K}$, we give a fast, deterministic algorithm for finding the Hermite normal form of $\mathbf{F}$ with complexity…
Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…
Universal quantum computation using optical coherent states is studied. A teleportation scheme for a coherent-state qubit is developed and applied to gate operations. This scheme is shown to be robust to detection inefficiency.
Standard quantum theory represents a composite system at a given time by a joint state, but it does not prescribe a joint state for a composite of systems at different times. If a more even-handed treatment of space and time is possible,…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are…
In quantum information and communication, optical schemes provide simple and intuitive experimental implementations. Of particular importance is quantum state preparation. In this thesis, the creation of polarisation entanglement using a…
A Hermitian quantum phase operator is formulated that mirrors the classical phase variable with proper time dependence and satisfies trigonometric identities. The eigenstates of the phase operator are solved in terms of Gegenbauer…
We describe an algorithm for quantum state tomography that converges in polynomial time to an estimate, together with a rigorous error bound on the fidelity between the estimate and the true state. The result suggests that state tomography…
We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
A new model of quantum computing has recently been proposed which, in analogy with a classical lambda-calculus, exploits quantum processes which operate on other quantum processes. One such quantum meta-operator takes N unitary…
We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable positive operator valued measurement (POVM) on a finite number of…