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Title: Entanglement universality of two-qubit X-states

We demonstrate that for every two-qubit state there is a X-counterpart, i.e., a corresponding two-qubit X-state of same spectrum and entanglement, as measured by concurrence, negativity or relative entropy of entanglement. By parametrizing the set of two-qubit X-states and a family of unitary transformations that preserve the sparse structure of a two-qubit X-state density matrix, we obtain the parametric form of a unitary transformation that converts arbitrary two-qubit states into their X-counterparts. Moreover, we provide a semi-analytic prescription on how to set the parameters of this unitary transformation in order to preserve concurrence or negativity. We also explicitly construct a set of X-state density matrices, parametrized by their purity and concurrence, whose elements are in one-to-one correspondence with the points of the concurrence versus purity (CP) diagram for generic two-qubit states. - Highlights: • Parametrization of separable, entangled and rank-specific two-qubit X-states. • Construction of a set of two-qubit X-states exhausting a two-qubit CP-diagram. • Parametrization of a disentangling unitary transformation for any two-qubit X-state. • Unitary transformation of any two-qubit state into a X-state of same entanglement.
Authors:
 [1] ;  [2] ;  [3]
  1. ARC Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St. Lucia, Queensland 4072 (Australia)
  2. Avenida General Osório 414, centro, 14.870-100 Jaboticabal, SP (Brazil)
  3. Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, 01140-070 São Paulo, SP (Brazil)
Publication Date:
OSTI Identifier:
22403462
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 351; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY MATRIX; ENTROPY; QUANTUM ENTANGLEMENT; QUANTUM STATES; QUBITS; UNITARITY