D. Salgado

Inductive entanglement classification of four qubits under stochastic local operations and classical communication

Using an inductive approach to classify multipartite entangled states under stochastic local operations and classical communication introduced recently by the authors [Phys. Rev. A 74, 052336 (2006)], we give the complete classification of four-qubit entangled pure states. Apart from the expected degenerate classes, we show that there exist eight inequivalent ways to entangle four qubits. In this respect, permutation symmetry is taken into account and states with a structure differing only by parameters inside a continuous set are considered to belong to the same class.

Inductive classification of multipartite entanglement under stochastic local operations and classical communication

L. Lamata, ∗ J. León, † D. Salgado, ‡ and E. Solano§3, 4, ¶ Instituto de Matemáticas y F́ısica Fundamental, CSIC, Serrano 113-bis, 28006 Madrid, Spain Dpto. F́ısica Teórica, Universidad Autónoma de Madrid, 28049 Cantoblanco, Madrid, Spain Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany Sección F́ısica, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Apartado Postal 1761, Lima, Peru (Dated: May 30, 2020)

Sequential Implementation of Global Quantum Operations

We study the possibility for a global unitary applied on an arbitrary number of qubits to be decomposed in a sequential unitary procedure, where an ancillary system is allowed to interact only once with each qubit. We prove that sequential unitary decompositions are in general impossible for genuine entangling operations, even with an infinite-dimensional ancilla, being the controlled-NOT gate a paradigmatic example. Nevertheless, we find particular nontrivial operations in quantum information that can be performed in a sequential unitary manner, as is the case of quantum error correction and quantum cloning.

Sequential quantum cloning.

Not all unitary operations upon a set of qubits can be implemented by sequential interactions between each qubit and an ancillary system. We analyze the specific case of sequential quantum cloning, 1-->M, and prove that the minimal dimension D of the ancilla grows linearly with the number of clones M. In particular, we obtain D=2M for symmetric universal quantum cloning and D=M+1 for symmetric phase-covariant cloning. Furthermore, we provide a recipe for the required ancilla-qubit interactions in each step of the sequential procedure for both cases.

A Simple Proof of the Jamiołkowski Criterion for Complete Positivity of Linear Maps

We give a simple direct proof of the Jamiołkowski criterion to check whether a linear map between matrix algebras is completely positive or not. This proof is more accessible for physicists than other ones found in the literature and provides a systematic method to give any set of Kraus matrices of the Kraus decomposition.

Spin entanglement loss by local correlation transfer to the momentum

7 pages, 7 figures.-- PACS nrs.: 03.67.Mn, 03.65.Yz, 03.65.Ud.-- ArXiv pre-print available at: http://arxiv.org/abs/quant-ph/0603225

QSES's and the Quantum Jump

Abstract The stochastic methods in Hilbert space have been used both from a fundamental and a practical point of view. The result reported here concerns the application of these methods to model the evolution of quantum systems and does not enter into the question of their fundamental or practical status. It can easily be stated as follows: Once a quantum stochastic evolution scheme is assumed, the incompatibility of the Markov property with the notion of quantum jumps is easily established