Thermodynamics of the n-level system in the planar isotropic Ising model with annealed bonds

1991 ◽  
Vol 178 (3) ◽  
pp. 528-550
Author(s):  
M.L. Polyakov
Keyword(s):  
Ising Model ◽  
Level System ◽  
N Level

scholarly journals Intuitionistic Quantum Logic of an n-level System

2009 ◽  
Vol 39 (7) ◽  
pp. 731-759 ◽  
Author(s):  
Martijn Caspers ◽  
Chris Heunen ◽  
Nicolaas P. Landsman ◽  
Bas Spitters
Keyword(s):  
Quantum Logic ◽  
Level System ◽  
N Level

scholarly journals REDUCED DYNAMICS FROM THE UNITARY GROUP TO SOME FLAG MANIFOLDS: INTERACTING MATRIX RICCATI EQUATIONS

2009 ◽  
Vol 06 (04) ◽  
pp. 573-581 ◽  
Author(s):  
KAZUYUKI FUJII ◽  
HIROSHI OIKE
Keyword(s):  
Differential Equations ◽  
Riccati Equation ◽  
Time Evolution ◽  
Unitary Group ◽  
Natural Generalization ◽  
Flag Manifolds ◽  
Level System ◽  
Nonlinear Superposition ◽  
N Level ◽  
Nonlinear Superposition Formula

In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equation satisfies. Our result is a natural generalization of the paper Chaturvedi et al. [1] (arXiv: 0706.0964 [quant-ph]).

On entanglement distillation and quantum error correction for unknown states and channels

Open Physics ◽  
2003 ◽  
Vol 1 (4) ◽  
Author(s):  
Pawel Horodecki
Keyword(s):  
Quantum State ◽  
Transmission Rate ◽  
Single Copy ◽  
Quantum Error Correction ◽  
Quantum Channels ◽  
Level System ◽  
Open Problems ◽  
Single Qubit ◽  
N Level ◽  
Quantum Error

AbstractWe consider the problem of invariance of distillable entanglement D and quantum capacities Q under erasure of information about single copy of quantum state or channel respectively. We argue that any 2 ⊗N two-way distillable state is still two-way distillable after erasure of single copy information. For some known distillation protocols the obtained two-way distillation rate is the same as if Alice and Bob knew the state from the very beginning. The isomorphism between quantum states and quantum channels is also investigated. In particular it is pointed out that any transmission rate down the channel is equal to distillation rate with formal LOCC-like superoperator that uses in general nonphysical Alice actions. This allows to we prove that if given channel Λ has nonzero capacity (Q → or Q ⟺) then the corresponding quantum state ϱ(Λ) has nonzero distillable entanglement (D → or D ⟺). Follwoing the latter arguments are provided that any channel mapping single qubit into N level system allows for reliable two-way transmission after erasure of information about single copy. Some open problems are discussed.

N‐level system in contact with a singular reservoir

1976 ◽  
Vol 17 (7) ◽  
pp. 1298-1305 ◽  
Author(s):  
Vittorio Gorini ◽  
Andrzej Kossakowski
Keyword(s):  
Level System ◽  
N Level

scholarly journals On Families of Wigner Functions for N-Level Quantum Systems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1013
Author(s):  
Vahagn Abgaryan ◽  
Arsen Khvedelidze
Keyword(s):  
Flag Manifold ◽  
Quantum Systems ◽  
Master Equations ◽  
Wigner Functions ◽  
Level System ◽  
Single Qubit ◽  
N Level ◽  
Weyl Correspondence ◽  
Quasiprobability Distributions ◽  
Complex Flag

A method for constructing all admissible unitary non-equivalent Wigner quasiprobability distributions providing the Stratonovic-h-Weyl correspondence for an arbitrary N-level quantum system is proposed. The method is based on the reformulation of the Stratonovich–Weyl correspondence in the form of algebraic “master equations” for the spectrum of the Stratonovich–Weyl kernel. The later implements a map between the operators in the Hilbert space and the functions in the phase space identified by the complex flag manifold. The non-uniqueness of the solutions to the master equations leads to diversity among the Wigner quasiprobability distributions. It is shown that among all possible Stratonovich–Weyl kernels for a N=(2j+1)-level system, one can always identify the representative that realizes the so-called SU(2)-symmetric spin-j symbol correspondence. The method is exemplified by considering the Wigner functions of a single qubit and a single qutrit.

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