QUANTUM OPTICS NETWORKS, UNITARY OPERATORS AND COMPUTER ALGEBRA

2008 ◽  
Vol 19 (07) ◽  
pp. 1069-1078 ◽  
Author(s):  
WILLI-HANS STEEB ◽  
YORICK HARDY
Keyword(s):  
Quantum Optics ◽  
Computer Algebra ◽  
Matrix Multiplication ◽  
Phase Shifters ◽  
Unitary Operators ◽  
Unitary Matrices ◽  
Creation And Annihilation Operators ◽  
Beam Splitters ◽  
Linear Quantum

In linear quantum optics we consider phase shifters, beam splitters, displacement operations, squeezing operations etc. The evolution can be described by unitary operators using Bose creation and annihilation operators. This evolution can be reduced to matrix multiplication using unitary matrices. We derive these evolutions for the different unitary operators. Finally a computer algebra implementation is provided.

UNITARY OPERATORS, ENTANGLEMENT, AND GRAM–SCHMIDT ORTHOGONALIZATION

2009 ◽  
Vol 20 (06) ◽  
pp. 891-899
Author(s):  
YORICK HARDY ◽  
WILLI-HANS STEEB
Keyword(s):  
Quantum Computing ◽  
Computer Algebra ◽  
Hilbert Spaces ◽  
Unitary Transformation ◽  
Unitary Operator ◽  
Unitary Operators ◽  
Unitary Matrices ◽  
Finite Dimensional ◽  
Schmidt Orthogonalization

We consider finite-dimensional Hilbert spaces [Formula: see text] with [Formula: see text] with n ≥ 2 and unitary operators. In particular, we consider the case n = 2m, where m ≥ 2 in order to study entanglement of states in these Hilbert spaces. Two normalized states ψ and ϕ in these Hilbert spaces [Formula: see text] are connected by a unitary transformation (n×n unitary matrices), i.e. ψ = Uϕ, where U is a unitary operator UU* = I. Given the normalized states ψ and ϕ, we provide an algorithm to find this unitary operator U for finite-dimensional Hilbert spaces. The construction is based on a modified Gram–Schmidt orthonormalization technique. A number of applications important in quantum computing are given. Symbolic C++ is used to give a computer algebra implementation in C++.

scholarly journals Crossed graphene nanoribbons as beam splitters and mirrors for electron quantum optics

2020 ◽  
Vol 102 (3) ◽  
Author(s):  
Sofia Sanz ◽  
Pedro Brandimarte ◽  
Géza Giedke ◽  
Daniel Sánchez-Portal ◽  
Thomas Frederiksen
Keyword(s):  
Quantum Optics ◽  
Graphene Nanoribbons ◽  
Beam Splitters ◽  
Electron Quantum

MONODROMY APPROACH TO QUANTUM COMPUTING

2002 ◽  
Vol 16 (30) ◽  
pp. 4593-4605 ◽  
Author(s):  
G. GIORGADZE
Keyword(s):  
Quantum Computing ◽  
Hilbert Problem ◽  
Holomorphic Vector Bundle ◽  
Classical System ◽  
Unitary Operators ◽  
Unitary Matrices ◽  
Classical Procedure ◽  
Logarithmic Singularities ◽  
The Given ◽  
Riemann Hilbert Problem

In this work, a gauge approach to quantum computing is considered. It is assumed that there exists a classical procedure for placing certain classical system in a state described by a holomorphic vector bundle with connection with logarithmic singularities. This bundle and its connection are constructed with the aid of unitary operators realizing the given algorithm using methods of the monodromic Riemann–Hilbert problem. Universality is understood in the sense that for any collection of unitary matrices there exists a connection with logarithmic singularities whose monodromy representation involves these matrices.

Generation of cluster-type entangled coherent states using weak nonlinearities

2011 ◽  
Vol 11 (1&2) ◽  
pp. 124-141
Author(s):  
Nguyen B. An ◽  
Kisik Kim ◽  
Jaewan Kim
Keyword(s):  
Coherent States ◽  
Single Photon ◽  
Optical Devices ◽  
Phase Shifters ◽  
Intense Laser ◽  
Laser Beams ◽  
Beam Splitters ◽  
Photo Detectors ◽  
Cluster Type ◽  
Entangled Coherent States

We propose a scheme to generate a recently introduced type of entangled coherent states using realistic weak cross-Kerr nonlinearities and intense laser beams. An intense laser can be filtered to make a faint one to be used for production of a single photon which is necessary in our scheme. The optical devices used are conventional ones such as interferometer, mirrors, beam-splitters, phase-shifters and photo-detectors. We also provide a detailed analysis on the effects of possible imperfections and decoherence showing that our scheme is robust against such effects.

scholarly journals Ultra-broadband silicon photonics devices based on subwavelength metamaterials -INVITED

2020 ◽  
Vol 238 ◽  
pp. 01002
Author(s):  
A. V. Velasco ◽  
D. González-Andrade ◽  
A. Herrero-Bermello ◽  
J. M. Luque-González ◽  
R. Halir ◽  
...  
Keyword(s):  
Optical Properties ◽  
Silicon Photonics ◽  
Building Blocks ◽  
Photonic Devices ◽  
Phase Shifters ◽  
Beam Splitters ◽  
Wide Range ◽  
Recent Developments ◽  
Photonics Devices

Subwavelength structured waveguides provide tailorable optical properties that can be leveraged to overcome bandwidth limitations in a wide range of photonic devices. In this invited talk, we present an overview of recent developments on subwavelength engineered building blocks, including phase shifters, mode multiplexers, polarization beam splitters and zero-birefringence waveguides.

Quantum optics of lossy beam splitters

1998 ◽  
Vol 57 (3) ◽  
pp. 2134-2145 ◽  
Author(s):  
Stephen M. Barnett ◽  
John Jeffers ◽  
Alessandra Gatti ◽  
Rodney Loudon
Keyword(s):  
Quantum Optics ◽  
Beam Splitters

Quantum teleportation of a tripartite entangled coherent state

2021 ◽  
Author(s):  
Shivani A. Kumar
Keyword(s):  
Coherent State ◽  
Quantum Channel ◽  
Quantum Teleportation ◽  
Optical Devices ◽  
Phase Shifters ◽  
Quantum Model ◽  
Beam Splitters ◽  
Entangled Coherent State ◽  
Linear Optical

The present work proposes a scheme to teleport a tripartite coherent state using an unparalleled four-component state as a quantum channel. The scheme involves linear optical devices like beam splitters and phase shifters. It is shown that, even by taking an uncompromising quantum model, almost a complete teleportation can be achieved with an impressive number of photons. It is also shown that the teleportation fails only if zero photons are found in all the three output modes or zero in two output modes and a nonzero even/odd photon in one mode. However, the probability of getting these output modes is almost negligible.

IMPROVING THE TELEPORTATION OF TRIPARTITE ENTANGLED COHERENT STATES IN CONTINUOUS VARIABLE

2009 ◽  
Vol 07 (01) ◽  
pp. 313-321 ◽  
Author(s):  
YONG SUN ◽  
BEN-JIN SUN ◽  
MEI-LI SHI ◽  
ZHONG-XIAO MAN ◽  
YUN-JIE XIA
Keyword(s):  
Coherent State ◽  
Continuous Variable ◽  
Phase Shifters ◽  
Entangled State ◽  
Quantum Channels ◽  
Average Fidelity ◽  
Beam Splitters ◽  
Entangled Coherent State ◽  
Tripartite Entangled State ◽  
Photo Detectors

We propose a feasible scheme for the quantum teleportation of tripartite entangled coherent state in terms of linear optical devices such as beam splitters, phase shifters and photo detectors. The scheme is based on the bipartite maximally entangled coherent state and the tripartite entangled coherent state with bipartite maximal entanglement as quantum channels. It shows that for an appreciable mean number of photons equal to 2, the total minimum of average fidelity for an arbitrary tripartite entangled state is 0.981684.

scholarly journals Quantum optics of lossy asymmetric beam splitters

2016 ◽  
Vol 24 (15) ◽  
pp. 16440 ◽  
Author(s):  
Ravitej Uppu ◽  
Tom A. W. Wolterink ◽  
Tristan B. H. Tentrup ◽  
Pepijn W. H. Pinkse
Keyword(s):  
Quantum Optics ◽  
Beam Splitters
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