Gaussian (N, z)-generalized Yang-Baxter operators

2016 ◽  
pp. 105-114
Author(s):  
Eric Rowell
Keyword(s):  
Bell States ◽  
Entangled States ◽  
Unitary Matrix ◽  
Baxter Equation ◽  
Careful Study ◽  
Standard Measurement ◽  
Measurement Basis ◽  
Parameter Dependent

We find unitary matrix solutions R˜(a) to the (multiplicative parameter-dependent) (N, z)-generalized Yang-Baxter equation that carry the standard measurement basis to m-level N-partite entangled states that generalize the 2-level bipartite entangled Bell states. This is achieved by a careful study of solutions to the Yang-Baxter equation discovered by Fateev and Zamolodchikov in 1982.

scholarly journals Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation

2020 ◽  
Vol 20 (1&2) ◽  
pp. 37-64
Author(s):  
Pramod Padmanabhan ◽  
Fumihiko Sugino ◽  
Diego Trancanelli
Keyword(s):  
Quantum Entanglement ◽  
Communication Protocol ◽  
Quantum Information Theory ◽  
Entangled States ◽  
Baxter Equation ◽  
Classical Communication ◽  
Separable States ◽  
Qubit System ◽  
Large Families ◽  
Parameter Dependent

Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding operators as quantum entanglers, and is part of a larger speculated connection between topological and quantum entanglement. We push the analysis of this connection forward, by showing that supersymmetry algebras can be used to construct large families of solutions of the spectral parameter-dependent generalized Yang-Baxter equation. We present a number of explicit examples and outline a general algorithm for arbitrary numbers of qubits. The operators we obtain produce, in turn, all the entangled states in a multi-qubit system classified by the Stochastic Local Operations and Classical Communication protocol introduced in quantum information theory.

QUANTUM TELEPORTATION OF AN ARBITRARY N-QUBIT STATE VIA NON-MAXIMALLY ENTANGLED STATE

2007 ◽  
Vol 05 (05) ◽  
pp. 673-683 ◽  
Author(s):  
YU-LING LIU ◽  
ZHONG-XIAO MAN ◽  
YUN-JIE XIA
Keyword(s):  
Quantum Teleportation ◽  
Success Probability ◽  
Qubit State ◽  
Bell States ◽  
Entangled State ◽  
Quantum Channels ◽  
Maximally Entangled State ◽  
Ghz States ◽  
Measurement Basis ◽  
Unit Probability

We explicitly present two schemes for quantum teleportation of an arbitrary N-qubit entangled state using, respectively, non-maximally entangled Bell states and GHZ states as the quantum channels, and generalized Bell states as the measurement basis. The scheme succeeds with unit fidelity but less than unit probability. By introducing additional qubit and unitary operations, the success probability of these two schemes can be increased.

scholarly journals ON TYPE I QUANTUM AFFINE SUPERALGEBRAS

1995 ◽  
Vol 10 (23) ◽  
pp. 3259-3281 ◽  
Author(s):  
GUSTAV W. DELIUS ◽  
MARK D. GOULD ◽  
JON R. LINKS ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Spectral Parameter ◽  
Lie Superalgebras ◽  
Baxter Equation ◽  
Type I ◽  
Free Fermion ◽  
General Technique ◽  
Finite Dimensional ◽  
Quantum Deformations ◽  
Free Fermion Model ◽  
Parameter Dependent

The type I simple Lie superalgebras are sl(m|n) and osp(2|2n). We study the quantum deformations of their untwisted affine extensions Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We identify additional relations between the simple generators (“extra q Serre relations”) which need to be imposed in order to properly define Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We present a general technique for deriving the spectral-parameter-dependent R matrices from quantum affine superalgebras. We determine the R matrices for the type I affine superalgebra Uq[sl(m|n)(1)] in various representations, thereby deriving new solutions of the spectral-parameter-dependent Yang-Baxter equation. In particular, because this algebra possesses one-parameter families of finite-dimensional irreps, we are able to construct R matrices depending on two additional spectral-parameter-like parameters, providing generalizations of the free fermion model.

REALIZATION OF FRT ALGEBRA RELATED TO A COLORED BRAID GROUP REPRESENTATION

1994 ◽  
Vol 09 (29) ◽  
pp. 2733-2743 ◽  
Author(s):  
B. BASU-MALLICK
Keyword(s):  
Braid Group ◽  
Group Representation ◽  
Toda Chain ◽  
Baxter Equation ◽  
Color Parameter ◽  
Triangular Matrices ◽  
Explicit Realization ◽  
Lower Triangular ◽  
Parameter Dependent ◽  
Lower Triangular Matrices

A colored braid group representation (CBGR) is constructed by using some modified universal ℛ-matrix associated with U q( gl (2)) quantized algebra. Explicit realization of Faddeev–Reshetikhin–Takhtajan (FRT) algebra, involving color parameter dependent upper and lower triangular matrices, is built up for this CBGR and subsequently applied to generate nonadditive type solutions of quantum Yang–Baxter equation. Rational limit of such solutions interestingly yields 'colored' extension of known Lax operators associated with lattice nonlinear Schrödinger model and Toda chain.

scholarly journals Topological field theory approach to intermediate statistics

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Ward Vleeshouwers ◽  
Vladimir Gritsev
Keyword(s):  
Simons Theory ◽  
Unitary Matrix ◽  
Local Order ◽  
Theory Approach ◽  
Localization Transition ◽  
The Matrix ◽  
Random Matrix Models ◽  
Topological Field ◽  
Parameter Dependent ◽  
Physical Phenomena

Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are characterized by the spectral form factor (SFF). Here, we calculate the SFF of unitary matrix ensembles of infinite order with the weight function satisfying the assumptions of Szeg"{o}’s limit theorem. We then consider a parameter-dependent critical ensemble which has intermediate statistics characteristic of ergodic-to-nonergodic transitions such as the Anderson localization transition. This same ensemble is the matrix model of U(N)U(N) Chern-Simons theory on S^3S3, and the SFF of this ensemble is proportional to the HOMFLY invariant of (2n,2)(2n,2)-torus links with one component in the fundamental and one in the antifundamental representation. This is one example of a large class of ensembles with intermediate statistics arising from topological field and string theories. Indeed, the absence of a local order parameter suggests that it is natural to characterize ergodic-to-nonergodic transitions using topological tools, such as we have done here.

Robustness of multipartite entangled states for fermionic systems under noisy channels in non-inertial frames

2021 ◽  
Author(s):  
Kwang-Il Kim ◽  
Myong Chol Pak ◽  
Tae-Hyok Kim ◽  
Jong Chol Kim ◽  
Yong-Hae Ko ◽  
...  
Keyword(s):  
Bell States ◽  
Entangled States ◽  
Tripartite Entanglement ◽  
Noisy Channels ◽  
Ghz States ◽  
Phase Damping ◽  
Inertial Frames ◽  
Fermionic Systems ◽  
The Difference ◽  
Bit Flip

Abstract We investigate robustness of bipartite and tripartite entangled states for fermionic systems in non-inertial frames, which are under noisy channels. We consider two Bell states and two Greenberger-Horne-Zeilinger (GHZ) states, which possess initially the same amount of entanglement, respectively. By using genuine multipartite (GM) concurrence, we analytically derive the equations that determine the difference between the robustness of these locally unitarily equivalent states under the amplitude-damping channel. We find that tendency of the robustness for two GHZ states evaluated by using three-tangle τ and GM concurrence as measures of genuine tripartite entanglement is equal to each other. We also find that the robustness of two Bell states is equal to each other under the depolarizing, phase damping and bit flip channels, and that the same is true for two GHZ states.

Entangled states implemented by Bn group operators, including properties based on HS decompositions, separability and concurrence

2015 ◽  
Vol 13 (01) ◽  
pp. 1450045 ◽  
Author(s):  
Y. Ben-Aryeh
Keyword(s):  
Bell States ◽  
Entangled States ◽  
Mixed States ◽  
Large N ◽  
Classical Correlations ◽  
Computational Basis

The use of the Bn group operators is developed for implementing entangling processes for large n-qubits systems (n > 2). By operating with the Bn group operators on the computational basis of states, entangled states are obtained with properties analogous to those of the 2-qubits Bell states. Tracing any qubit from the 3-qubits Bn entangled states, we get mixed states which are separable with zero concurrence, and correspondingly with only classical correlations. These properties are generalized to larger Bn entangled states (n > 3). The properties of the Bn entangled states are analyzed by the use of Hilbert–Schmidt (HS) decompositions.

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