General superposition states associated to the rotational and inversion symmetries in the phase space
arXiv:2004.02645 · doi:10.1088/1402-4896/ab7feb
Abstract
The general quantum superposition states containing the irreducible representation of the -dimensional groups associated to the rotational symmetry of the -sided regular polygon i.e. the cyclic group ( ) and the rotational and inversion symmetries of the polygon, i.e. the dihedral group ( ) are defined and studied. It is shown that the resulting states form an -dimensional orthogonal set of states which can lead to the finite representation of specific systems. The correspondence between the symmetric states and the renormalized states, resulting from the selective erasure of photon numbers from an arbitrary, noninvariant initial state, is also established. As an example, the general cyclic Gaussian states are presented. The presence of nonclassical properties in these states as subpoissonian photon statistics is addressed. Also, their use in the calculation of physical quantities as the entanglement in a bipartite system is discussed.
References in corpus (20)
- Quantum Error Correction for Quantum Memories
- Quantum computation with optical coherent states
- Generation of a superposition of odd photon number states for quantum information networks
- Entangled coherent states: teleportation and decoherence
- Quantum channels and memory effects
- Quantum information processing for a coherent superposition state via a mixed entangled coherent channel
- Generation of Optical Coherent State Superpositions by Number-Resolved Photon Subtraction from Squeezed Vacuum
- Generation of large-amplitude coherent-state superposition via ancilla-assisted photon-subtraction
- Deterministic creation of entangled atom-light Schrödinger-cat states
- Schrodinger cats and their power for quantum information processing
- Maximal Violation of Bell Inequalities using Continuous Variables Measurements
- Quantum nonlocality test for continuous-variable states with dichotomic observables
- Squeezed States for General Systems
- Violation of Bell's inequality using classical measurements and non-linear local operations
- Quantum error correction against photon loss using multi-component cat states
- Coherent states on the circle
- Quantum Phase and Quantum Phase Operators: Some Physics and Some History
- Sampling Theorem and Discrete Fourier Transform on the Hyperboloid
- Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere
- Dynamic Generation of Light States with Discrete Symmetries