Canonical operators and the optimal concentration of three-qubit Greenberger-Horne-Zeilinger states
arXiv:1403.1123 · doi:10.1103/PhysRevA.89.032320
Abstract
It is well known that quantum states that can be transformed into each other by local unitary transformations are equal from the information theoretic point of view. This defines equivalence classes of states and allows one to write any state with the minimal number of parameters called the canonical form of the state. We define the equivalence classes of local measurements such that local operations which transform states from one equivalence class into another with the same probability are equivalent. This equivalence relation allows one to write the operators with the minimal number of parameters, which we call canonical operators, and hence the use of the canonical operators simplifies the optimal manipulation of quantum states. We use the canonical local operators for the concentration of three-qubit Greenberger-Horne-Zeilinger states and obtain the optimal concentration protocols in terms of the unitary invariants of quantum states, namely, the bipartite concurrences and the three-tangle.
arXiv comment15 pages, published version
References in corpus (23)
- Three qubits can be entangled in two inequivalent ways
- Concentrating Partial Entanglement by Local Operations
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Distributed Entanglement
- Conditions for a class of entanglement transformations
- Classification of mixed three-qubit states
- Generalized Schmidt decomposition and classification of three-quantum-bit states
- Perfect Teleportation and Superdense Coding With W-States
- Entanglement of pure states for a single copy
- Probabilistic teleportation and entanglement matching
- Efficient two-step entanglement concentration for arbitrary W states
- Deterministic secure direct communication using GHZ states and swapping quantum entanglement
- Probabilistic Quantum Teleportation
- Three-qubit pure-state canonical forms
- Optimal teleportation with a mixed state of two qubits
- Optimal distillation of a GHZ state
- Transformations of -Type Entangled States
- Optimal distillation of three-qubit W states
- Distillation of GHZ states by selective information manipulation
- Deterministic LOCC transformation of three-qubit pure states and entanglement transfer
- Bounds on probability of transformations between multi-partite pure states
- Optimal Entanglement Transformations Among N-qubit W-Class States
- Optimal Local Transformations of Flip and Exchange Symmetric Entangled States