Results 11  20
of
200
YangBaxterizations, universal quantum gates and Hamiltonians
 Quantum Inf. Process
"... The unitary braiding operators describing topological entanglements can be viewed as universal quantum gates for quantum computation. With the help of the Brylinski’s theorem, the unitary solutions of the quantum Yang–Baxter equation can be also related to universal quantum gates. This paper derives ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
(Show Context)
The unitary braiding operators describing topological entanglements can be viewed as universal quantum gates for quantum computation. With the help of the Brylinski’s theorem, the unitary solutions of the quantum Yang–Baxter equation can be also related to universal quantum gates. This paper derives unitary solutions of the quantum Yang–Baxter equation via Yang–Baxterization from the solutions of the braid relation. We study Yang–Baxterizations of the nonstandard and standard representations of the sixvertex model and the complete solutions of the nonvanishing eightvertex model. We construct Hamiltonians responsible for the timeevolution of the unitary braiding operators which lead to the Schrödinger equations.
Measures and dynamics of entangled states
, 2005
"... We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of a specific entanglement measure, concurrence, for further implementation in the monitoring of the time evolution of multipartite entanglement under incoherent environment coupling. The flexibility of the technical machinery established here is illustrated by its implementation for
Everything you always wanted to know about LOCC (but were afraid to ask
 Comm. Math. Phys
"... ar ..."
(Show Context)
A Study Of Entanglement In Quantum Information Theory
, 2002
"... Although the concept of quantum entanglement has been known for about seventy years, it only recently quit the realms of metatheoretical discussions when it was discovered how entanglement can be exploited to compute and communicate with an unprecedented power. The primary motivation of the work pr ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
Although the concept of quantum entanglement has been known for about seventy years, it only recently quit the realms of metatheoretical discussions when it was discovered how entanglement can be exploited to compute and communicate with an unprecedented power. The primary motivation of the work presented in this thesis has been to contribute to the big effort that has been done during the last decade to understand and quantify quantum entanglement. We have developed advanced techniques of linear and multilinear algebra to investigate and classify entangled pure and mixed quantum states, and discussed some novel applications in the field of quantum information theory. The results presented in this thesis are mainly of interest from a fundamental point a view: entanglement is the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought [186]. It is however a real privilege that fundamental research in quantum information theory bears the tools of tomorrow's electrical engineers: the ongoing miniaturization of electronic components will soon reach a scale where quantum mechanical effects play a major role.
Distinguishability of Quantum States by Separable Operations
, 2007
"... We study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An analytical version of this condition is derived for the case ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An analytical version of this condition is derived for the case of (D − 1) pure states, where D is the total dimension of the state space under consideration. A number of interesting consequences of this result are then carefully investigated. Remarkably, we show there exists a large class of 2 ⊗ 2 separable operations not being realizable by local operations and classical communication. Before our work only a class of 3 ⊗ 3 nonlocal separable operations was known [Bennett et al, Phys. Rev. A 59, 1070 (1999)]. We also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of 1 or 2 orthogonal product states, i.e., has an orthogonal Schmidt number not less than 3, thus generalize the recent work about indistinguishable bipartite subspaces [Watrous, Phys. Rev. Lett. 95, 080505 (2005)]. Notably, we obtain an explicit construction of indistinguishable subspaces of dimension 7 (or 6) by considering a composite quantum system consisting of two qutrits (resp. three qubits), which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8.
Entanglement and its role in shor’s algorithm
 Quantum Inform. Comput
"... Abstract. Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor’s factoring algorithm, can achieve exponentially better performance than their classical counterparts. The nature of this resour ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Abstract. Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor’s factoring algorithm, can achieve exponentially better performance than their classical counterparts. The nature of this resource is still not fully understood: here we use numerical simulation to investigate how entanglement between register qubits varies as Shor’s algorithm is run on a quantum computer. The patterns in the entanglement are found to correlate with the choice of basis for the quantum Fourier transform rather than with any crucially quantum aspect of the algorithm. 1
Combinatorial laplacians and positivity under partial transpose
 Math. Struct. in Comp. Sci
"... Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein et al. Phys. Rev. A, 73:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix carries a block structure with respect to which properties such as separability can ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
(Show Context)
Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein et al. Phys. Rev. A, 73:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix carries a block structure with respect to which properties such as separability can be considered. We prove that the socalled degreecriterion, which was conjectured to be necessary and sufficient for separability of density matrices of graphs, is equivalent to the PPTcriterion. Additionally, we give an alternative proof of the sufficiency of the degreecriterion when one of the array dimensions has length