Related papers: Fractional Hadamard transform with continuous vari…
A fast quantum search algorithm for continuous variables is presented. The result is the quantum continuous variable analog of Grover's algorithm originally proposed for qubits. A continuous variable analog of the Hadamard (i.e., Fourier…
The quantum Fourier transform for discrete variable (dvQFT) is an efficient algorithm for several applications. It is usually considered for the processing of quantum bits (qubits) and its efficient implementation is obtained with two…
Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type…
We describe a new version of continuous variables quantum holographic teleportation of optical images. Unlike the previously proposed scheme, it is based on the continuous variables quantum entanglement between the light fields of different…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
The positivity of the partial transpose is in general only a necessary condition for separability. There exist quantum states that are not separable, but nevertheless are positive under partial transpose. States of this type are known as…
We introduce a formalism of nonlinear canonical transformations for general systems of multiphoton quantum optics. For single-mode systems the transformations depend on a tunable free parameter, the homodyne local oscillator angle; for…
In their seminal paper, Caves and Schumaker presented a new formalism for quantum optics, intended to serve as a building block for describing two-photon processes, in terms of new, generalized qudratures. The important, revolutionary…
Multimode fibres offer the advantages of high resolution and miniaturization over single mode fibers in the field of optical imaging. However, multimode fibre's imaging is susceptible to perturbations of MMF that can lead to secondary…
The generating entangled state by using a 50/50 beamsplitter has been discussed in the literature before . In this paper we explore how to use an asymmetric beam-splitter to produce a new kind of entangled state. We construct such kind of…
A Generalised Hadamard Transform for multi-phase or multilevel signals is introduced, which includes the Fourier, Generalised, Discrete Fourier, Walsh-Hadamard and Reverse Jacket Transforms. The jacket construction is formalised and shown…
We provide a fast and simple method to solve fractional variational problems with dependence on Hadamard fractional derivatives. Using a relation between the Hadamard fractional operator and a sum involving integer-order derivatives, we…
Partial transpose is an important operation for quantifying the entanglement, here we study the (partial) transpose of any single (two-mode) operators. Using the Fock-basis expansion, it is found that the transposed operator of an arbitrary…
We present a theory of entanglement transformations of Gaussian pure states with local Gaussian operations and classical communication. This is the experimentally accessible set of operations that can be realized with optical elements such…
Two-mode squeezed states, which are entangled states with bipartite quantum correlations in continuous-variable systems, are crucial in quantum information processing and metrology. Recently, continuous-variable quantum computing with the…
We show that partial transposition for pure and mixed two-particle states in a discrete $N$-dimensional Hilbert space is equivalent to a change in sign of a "momentum-like" variable of one of the particles in the Wigner function for the…
We introduce a new class of unitary transformations based on the su(1,1) Lie algebra that generalizes, for certain particular representations of its generators, well-known squeezing transformations in quantum optics. To illustrate our…
We investigate how entanglement can be transferred between continuous variable and qubit systems. We find that a two-mode squeezed vacuum state and a continuous variable Werner state can be converted to the product states of infinitive…
We develop a new method of representation of quantum states in terms of the displaced number states. We call it representation, where is an amplitude of the base displaced states. In particular, representation was obtained for set of the…