Noisy entanglement evolution for graph states
arXiv:1006.3152 · doi:10.1103/PhysRevA.82.032317
Abstract
A general method for the study of the entanglement evolution of graph states under the action of Pauli was recently proposed in [Cavalcanti, et al., Phys. Rev. Lett. 103, 030502 (2009)]. This method is based on lower and upper bounds on the entanglement of the entire state as a function only of the state of a considerably-smaller subsystem, which undergoes an effective noise process. This provides a huge simplification on the size of the matrices involved in the calculation of entanglement in these systems. In the present paper we elaborate on this method in details and generalize it to other natural situations not described by Pauli maps. Specifically, for Pauli maps we introduce an explicit formula for the characterization of the resulting effective noise. Beyond Pauli maps, we show that the same ideas can be applied to the case of thermal reservoirs at arbitrary temperature. In the latter case, we discuss how to optimize the bounds as a function of the noise strength. We illustrate our ideas with explicit exemplary results for several different graphs and particular decoherence processes. The limitations of the method are also discussed.
13 pages, 8 figures. v2: published version
References in corpus (31)
- Quantum entanglement
- A computable measure of entanglement
- Quantum secret sharing
- Quantum-enhanced measurements: beating the standard quantum limit
- Measurement-based quantum computation with cluster states
- Experimental One-Way Quantum Computing
- Measurement-based quantum computation
- Multi-party entanglement in graph states
- A Multiparticle Generalization of Entanglement Swapping
- Entanglement monotones
- Experimental entanglement of six photons in graph states
- Quantum error-correcting codes associated with graphs
- Stability of macroscopic entanglement under decoherence
- Experimental Analysis of a 4-Qubit Cluster State
- Scaling laws for the decay of multiqubit entanglement
- Multiparticle entanglement purification for graph states
- Experimental realization of one-way quantum computing with two-photon four-qubit cluster states
- Entanglement properties of multipartite entangled states under the influence of decoherence
- Quantum computation based on d-level cluster states
- Robustness of Multi-Party Entanglement
- Multiparticle entanglement purification for two-colorable graph states
- Multiparticle entanglement under the influence of decoherence
- Active one-way quantum computation with 2-photon 4-qubit cluster states
- Open-system dynamics of graph-state entanglement
- Separable Operations on Pure States
- Nonlocal Entanglement Transformations Achievable by Separable Operations
- Scalability of GHZ and random-state entanglement in the presence of decoherence
- Multipartite secure state distribution
- Macroscopic bound entanglement in thermal graph states
- Noise models for superoperators in the chord representation
- Decoherence-based exploration of d-dimensional one-way quantum computation
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- Open-System Dynamics of Entanglement
- Macroscopic quantum states: measures, fragility and implementations
- Robustness of Entanglement as a Resource
- Noisy One-Way Quantum Computations: The Role of Correlations
- Time-invariant entanglement and sudden death of nonlocality for multipartite systems under collective dephasing
- Multipartite quantum nonlocality under local decoherence
- Gapped Two-Body Hamiltonian for continuous-variable quantum computation
- Dissociation and annihilation of multipartite entanglement structure in dissipative quantum dynamics
- Dynamics of genuine multipartite entanglement under local non-Markovian dephasing
- Robustness of multiparticle entanglement: specific entanglement classes and random states
- Superoperator Analysis of Entanglement in a Four-Qubit Cluster State
- Detecting nonlocality of noisy multipartite states with the CHSH inequality
- Estimating localizable entanglement from witnesses
- Qubit-Qutrit () quantum systems: An investigation of some quantum correlations under collective dephasing
- Linear-optical simulation of the cooling of a cluster-state Hamiltonian system
- Graph state basis for Pauli Channels
- Macroscopic Schrödinger Cat Resistant to Particle Loss and Local Decoherence
- Genuine entanglement under squeezed generalized amplitude damping channels with memory
- Optimal correction of independent and correlated errors
- Localizing genuine multiparty entanglement in noisy stabilizer states
- Exact dynamics of single qubit gate fidelities under the measurement-based quantum computation scheme
- Sudden change of genuine multipartite entanglement in non-Markovian dynamics