Related papers: Squeezed states in the quaternionic setting
Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that various classes of coherent states such as the canonical coherent states, pure squeezed states, fermionic coherent states can be defined…
A set of reproducing kernel Hilbert spaces are obtained on Hilbert spaces over quaternion slices with the aid of coherent states. It is proved that the so obtained set forms a measurable field of Hilbert spaces and their direct integral…
A state in a d-dimensional Hilbert space can be simulated by a state defined in a different dimension with high fidelity. We assess how faithfully such the approximated state can perform quantum protocols, using an example of the squeezed…
In these notes, we discuss squeezed states using the elementary quantum language based on one-dimensional Schr\"odinger equation. No operators are used. The language of quantum optics is mentioned only for a hint to solve a differential…
The squeezed states are states of minimum uncertainty, but unlike the coherent states, in which the uncertainty in the position and the momentum are the same, these allow to reduce the uncertainty, either in the position or in the momentum,…
We show that spin squeezing implies pairwise entanglement for arbitrary symmetric multiqubit states. If the squeezing parameter is less than or equal to 1, we demonstrate a quantitative relation between the squeezing parameter and the…
In the second part of our review (for the first part see quant-ph/0108080), we discuss a physical model for generation of "truncated" coherent and squeezed states in finite-dimensional Hibert spaces.
A general algorithm has been given for the generation of Coherent and Squeezed states, in one-dimensional hamiltonians with shape invariant potential, obtained from the master function. The minimum uncertainty states of these potentials are…
In this paper we treat coherent-squeezed states of Fock space once more and study some basic properties of them from a geometrical point of view. Since the set of coherent-squeezed states $\{\ket{\alpha, \beta}\ |\ \alpha, \beta \in…
We define and study the properties of ``squeezed quantum multiplets''. Ordinary multiplets are sets of $D$-orthonormal quantum states formed by superpositions of states squeezed along $D$ equally spaced directions in quadrature space. More…
Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart. With the aid of the…
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…
Quantisation with Gaussian type states offers certain advantages over other quantisation schemes, in particular, they can serve to regularise formally discontinuous classical functions leading to well defined quantum operators. In this work…
Particle distributions in squeezed states, even and odd coherent states are given in terms of multivariable Hermite polynomials. The Q--function and Wigner function for nonclassical field states are discussed.
A parity-dependent squeezing operator is introduced which imposes different SU(1,1) rotations on the even and odd subspaces of the harmonic oscillator Hilbert space. This operator is used to define parity-dependent squeezed states which…
It is shown that the time evolution of the squeezed and displaced state may be obtained by solving the Heisenberg equation of motion of an appropriate operator and finding the eigenstates of the time evolved operator. The connection between…
Quantum entanglement between particles is expected to allow one to perform tasks that would otherwise be impossible. In quantum sensing and metrology, entanglement is often claimed to enable a precision that cannot be attained with the same…
The fundamental properties of recently introduced stretched coherent states are investigated. It has been shown that stretched coherent states retain the fundamental properties of standard coherent states and generalize the resolution of…
It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all N-party pure states is…
For a charged particle in a homogeneous magnetic field, we construct stationary squeezed states which are eigenfunctions of the Hamiltonian and the non-Hermitian operator $\hat{X}_{\Phi} = \hat{X} \cos \Phi + \hat{Y} \sin \Phi$, $\hat{X}$…