Nonlocal unambiguous discrimination among N nonorthogonal qudit states lying in a higher-dimensional Hilbert space

2011 ◽  
Vol 55 (1) ◽  
pp. 55-59 ◽  
Author(s):  
LiBing Chen ◽  
Hong Lu
Keyword(s):  
Hilbert Space ◽  
Unambiguous Discrimination ◽  
Dimensional Hilbert Space ◽  
Higher Dimensional

Simplifying Schmidt number witnesses via higher-dimensional embeddings

2004 ◽  
Vol 4 (3) ◽  
pp. 207-221
Author(s):  
F. Hulpke ◽  
D. Bruss ◽  
M. Levenstein ◽  
A. Sanpera
Keyword(s):  
Hilbert Space ◽  
Schmidt Number ◽  
Convex Sets ◽  
Entanglement Witness ◽  
Simple Method ◽  
Dimensional Hilbert Space ◽  
Higher Dimensional ◽  
Arbitrary Convex

We apply the generalised concept of witness operators to arbitrary convex sets, and review the criteria for the optimisation of these general witnesses. We then define an embedding of state vectors and operators into a higher-dimensional Hilbert space. This embedding leads to a connection between any Schmidt number witness in the original Hilbert space and a witness for Schmidt number two (i.e. the most general entanglement witness) in the appropriate enlarged Hilbert space. Using this relation we arrive at a conceptually simple method for the construction of Schmidt number witnesses in bipartite systems.

A NEW PROOF OF NONEXISTENCE OF PROBABILISTIC QUANTUM CLONING MACHINE

2007 ◽  
Vol 05 (04) ◽  
pp. 611-616
Author(s):  
SAMIR KUNKRI ◽  
SUJIT K. CHOUDHARY
Keyword(s):  
Hilbert Space ◽  
Simple Proof ◽  
Causality Principle ◽  
Quantum Cloning ◽  
Dimensional Hilbert Space ◽  
Higher Dimensional ◽  
Probabilistic Quantum Cloning

We give a simple proof of the impossibility of probabilistic exact 1 → 2 cloning for any three different states of a qubit. The simplicity of the proof is due to the use of a stronger version of no violation of the causality principle. The proof is also extended to higher-dimensional Hilbert space, but for a special ensemble of states.

EXACT REMOTE STATE PREPARATION FOR MULTIPARTIES USING DARK STATES

2003 ◽  
Vol 01 (03) ◽  
pp. 301-319 ◽  
Author(s):  
P. AGRAWAL ◽  
P. PARASHAR ◽  
A. K. PATI
Keyword(s):  
Hilbert Space ◽  
Higher Dimensions ◽  
Remote State Preparation ◽  
Space Systems ◽  
Quantum Channels ◽  
Classical Communication ◽  
State Preparation ◽  
Dimensional Hilbert Space ◽  
Higher Dimensional

We discuss the exact remote state preparation (RSP) protocol of special ensembles of qubits at multiple locations. Generalization of this protocol for higher dimensional Hilbert space systems for multiparties is also presented. Using the "dark states", for multiparties in higher dimensions as quantum channels, we show several instances of remote state preparation protocol using multiparticle measurement and classical communication. We find that not all dark states can be used for exact remote state preparation, nevertheless any superposition of dark states can be used for exact RSP in a probabilistic manner.

scholarly journals Remote operations and interactions for systems of arbitrary-dimensional Hilbert space: State-operator approach

2002 ◽  
Vol 65 (3) ◽  
Author(s):  
Benni Reznik ◽  
Yakir Aharonov ◽  
Berry Groisman
Keyword(s):  
Hilbert Space ◽  
Operator Approach ◽  
State Operator ◽  
Dimensional Hilbert Space ◽  
Space State ◽  
Remote Operations

scholarly journals EXTENSION ALGEBRAS OF CUNTZ ALGEBRA, II

2009 ◽  
Vol 80 (1) ◽  
pp. 83-90 ◽  
Author(s):  
SHUDONG LIU ◽  
XIAOCHUN FANG
Keyword(s):  
Hilbert Space ◽  
Compact Operators ◽  
Cuntz Algebra ◽  
Infinite Dimensional ◽  
Algebra Ii ◽  
Infinite Dimensional Hilbert Space ◽  
Dimensional Hilbert Space ◽  
K Theory ◽  
Extension Algebra

AbstractIn this paper, we construct the unique (up to isomorphism) extension algebra, denoted by E∞, of the Cuntz algebra 𝒪∞ by the C*-algebra of compact operators on a separable infinite-dimensional Hilbert space. We prove that two unital monomorphisms from E∞ to a unital purely infinite simple C*-algebra are approximately unitarily equivalent if and only if they induce the same homomorphisms in K-theory.

scholarly journals Partial automorphisms of stable C*-algebras and Hilbert C*-bimodules

2005 ◽  
Vol 79 (3) ◽  
pp. 391-398
Author(s):  
Kazunori Kodaka
Keyword(s):  
Hilbert Space ◽  
Compact Operators ◽  
Equivalence Classes ◽  
Infinite Dimensional ◽  
C Algebras ◽  
Infinite Dimensional Hilbert Space ◽  
Dimensional Hilbert Space ◽  
Countably Infinite

AbstractLet A be a C*-algebra and K the C*-algebra of all compact operators on a countably infinite dimensional Hilbert space. In this note, we shall show that there is an isomorphism of a semigroup of equivalence classes of certain partial automorphisms of A ⊗ K onto a semigroup of equivalence classes of certain countably generated A-A-Hilbert bimodules.

Quantumness, generalized spherical 2-design, and symmetric informationally complete POVM

2007 ◽  
Vol 7 (8) ◽  
pp. 730-737
Author(s):  
I.H. Kim
Keyword(s):  
Hilbert Space ◽  
Lower Bound ◽  
Equivalence Relation ◽  
Open Problem ◽  
Natural Generalization ◽  
Quantum States ◽  
Minimal Set ◽  
Dimensional Hilbert Space

Fuchs and Sasaki defined the quantumness of a set of quantum states in \cite{Quantumness}, which is related to the fidelity loss in transmission of the quantum states through a classical channel. In \cite{Fuchs}, Fuchs showed that in $d$-dimensional Hilbert space, minimum quantumness is $\frac{2}{d+1}$, and this can be achieved by all rays in the space. He left an open problem, asking whether fewer than $d^2$ states can achieve this bound. Recently, in a different context, Scott introduced a concept of generalized $t$-design in \cite{GenSphet}, which is a natural generalization of spherical $t$-design. In this paper, we show that the lower bound on the quantumness can be achieved if and only if the states form a generalized 2-design. As a corollary, we show that this bound can be only achieved if the number of states are larger or equal to $d^2$, answering the open problem. Furthermore, we also show that the minimal set of such ensemble is Symmetric Informationally Complete POVM(SIC-POVM). This leads to an equivalence relation between SIC-POVM and minimal set of ensemble achieving minimal quantumness.

The Set of Finite Operators is Nowhere Dense

1989 ◽  
Vol 32 (3) ◽  
pp. 320-326 ◽  
Author(s):  
Domingo A. Herrero
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Dense Subset ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Dimensional Hilbert Space

AbstractA bounded linear operator A on a complex, separable, infinite dimensional Hilbert space is called finite if for each . It is shown that the class of all finite operators is a closed nowhere dense subset of

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