Entanglement universality of two-qubit X-states
arXiv:1407.3021 · doi:10.1016/j.aop.2014.08.017
Abstract
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.
24 pages, 6 figures. v2 includes new references and minor changes (accepted version)
References in corpus (9)
- Free-Space distribution of entanglement and single photons over 144 km
- Beating the channel capacity limit for linear photonic superdense coding
- Quantum teleportation using active feed-forward between two Canary Islands
- Genuinely Multipartite Concurrence of N-qubit X-matrices
- Entanglement Evolution in the Presence of Decoherence
- Closed formula for the relative entropy of entanglement
- Some Open Problems in Quantum Information Theory
- Closed formula for the relative entropy of entanglement in all dimensions
- Analytical formula connecting entangled state and the closest disentangled state
Cited by in corpus (8)
- Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix
- Maximally entangled mixed states for qubit-qutrit systems
- Entanglement of two hybrid optomechanical cavities composed of BEC atoms under Bell detection
- Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States
- Maximally genuine multipartite entangled mixed X-states of N-qubits
- Bounds on bipartite entanglement from fixed marginals
- Heuristic for estimation of multiqubit genuine multipartite entanglement
- Asymmetric steerability of quantum equilibrium and nonequilibrium steady states through entanglement detection