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.
arXiv comment24 pages, 6 figures. v2 includes new references and minor changes (accepted version)
References in corpus (45)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
- Mixed State Entanglement and Quantum Error Correction
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Concentrating Partial Entanglement by Local Operations
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Quantifying Entanglement
- Entanglement Measures and Purification Procedures
- On the volume of the set of mixed entangled states
- 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
- Thermodynamics and the Measure of Entanglement
- Experimental realisation of Shor's quantum factoring algorithm using qubit recycling
- Maximizing the entanglement of two mixed qubits
- Maximal entanglement versus entropy for mixed quantum states
- A comparison of entanglement measures
- Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement
- Maximally entangled mixed states of two qubits
- Quantum inseparability as local pseudomixture
- Maximally entangled mixed states in two qubits
- A comparison of the entanglement measures negativity and concurrence
- Genuinely Multipartite Concurrence of N-qubit X-matrices
- Maximally entangled mixed states: Creation and concentration
- Algebraic characterization of X-states in quantum information
- Detection of vacuum entanglement in a linear ion trap
- Continuity bounds for entanglement
- Ordering States with Entanglement Measures
- Asymptotic Relative Entropy of Entanglement for Orthogonally Invariant States
- Entanglement Evolution in the Presence of Decoherence
- Experimental preparation of Werner state via spontaneous parametric down-conversion
- Concurrence vs. purity: Influence of local channels on Bell states of two qubits
- Closed formula for the relative entropy of entanglement
- Quantum properties and dynamics of X states
- 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
- Generation of Werner states via collective decay of coherently driven atoms
- Quantification of entanglement by means of convergent iterations
- Evidence that All States Are Unitarily Equivalent to X States of the Same Entanglement
- Maximizing genuine multipartite entanglement of N mixed qubits
- Relative entropy of entanglement of a kind of two qubit entangled states
Cited by in corpus (38)
- On the quantum discord of general X states
- 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
- Calculation of quantum discord in arbitrary dimensions, especially for X- and other specialized states
- Entanglement harvesting in double-layer graphene by vacuum fluctuations in a microcavity
- Tri-partite non-maximally entangled mixed states as a resource for optimum controlled quantum teleportation fidelity
- Characterizing qubit channels in the context of quantum teleportation
- Fidelity deviation in quantum teleportation with a two-qubit state
- Attainable and usable coherence in X states over Markovian and non-Markovian channels
- On the discrete Wigner function for SU(N)
- Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer
- Necessary conditions for steerability of two qubits, from consideration of local operations
- Entanglement of two hybrid optomechanical cavities composed of BEC atoms under Bell detection
- Two-qubit mixed states and teleportation fidelity: Purity, concurrence, and beyond
- Separability Probability Formulas and Their Proofs for Generalized Two-Qubit X-Matrices Endowed with Hilbert-Schmidt and Induced Measures
- Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States
- Facets of correlated non-Markovian channels
- Maximally genuine multipartite entangled mixed X-states of N-qubits
- Bounds on bipartite entanglement from fixed marginals
- Master Lovas-Andai and Equivalent Formulas Verifying the Two-Qubit Hilbert-Schmidt Separability Probability and Companion Rational-Valued Conjectures
- Pairwise Concurrence in Cyclically Symmetric Quantum States
- Derivation of the robustness from the concurrence
- Heuristic for estimation of multiqubit genuine multipartite entanglement
- Local available quantum correlations of X states: The symmetric and anti-symmetric cases
- Local available quantum correlations of non-symmetric X states
- Entanglement Universality of TGX States in Qubit-Qutrit Systems
- Non-maximally entangled mixed states of X and non-X types as teleportation channels
- Response of macroscopic and microscopic dynamical quantifiers to the quantum critical region
- Formulas for Generalized Two-Qubit Separability Probabilities
- Two-Qubit Separability Probabilities as Joint Functions of the Bloch Radii of the Qubit Subsystems
- Experimental protocol for qubit-environment entanglement detection
- Multipartite Mixed Maximally Entangled States: Mixed States with Entanglement 1
- Controlling nonlocality of bipartite qubit states via quantum channels
- Representations of two-qubit and ququart states via discrete Wigner functions
- Comparing coherence measures for X states: Can quantum states be ordered based on quantum coherence?
- Asymmetric steerability of quantum equilibrium and nonequilibrium steady states through entanglement detection
- Local-available quantum correlation swapping in one-parameter X states
- Optimizing entanglement in two-qubit systems