Evolution and Symmetry of Multipartite Entanglement

Abstract

We discover a simple factorization law describing how multipartite entanglement of a composite quantum system evolves when one of the subsystems undergoes an arbitrary physical process. This multipartite entanglement decay is determined uniquely by a single factor we call the entanglement resilient factor (ERF). Since the ERF is a function of the quantum channel alone, we find that multipartite entanglement evolves in exactly the same way as bipartite (two qudits) entanglement. For the two qubits case, our factorization law reduces to the main result of Nature Physics 4, 99 (2008). In addition, for a permutation $P$, we provide an operational definition of $P$-asymmetry of entanglement, and find the conditions when a permuted version of a state can be achieved by local means.

5.1 pages, few typos fixed

References in corpus (4)

• Constructing N-qubit entanglement monotones from anti-linear operators
• A Factorization Law for Entanglement Decay
• On polynomial invariants of several qubits
• Entanglement evolution in finite dimensions

Cited by in corpus (29)

• Open-System Dynamics of Entanglement
• Quantifying entanglement resources
• Evolution equation for quantum coherence
• Classification of multipartite entanglement in all dimensions
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• Generalized Criterion of Maximally Multi-Qubit Entanglement
• Evolution equation for geometric quantum correlation measures
• Multipartite Entanglement Measure and Complete Monogamy Relation
• Genuine multipartite entanglement measure
• Robust entangled qutrit states in atmospheric turbulence
• Bipartite entanglement-annihilating maps: necessary and sufficient conditions
• A quantitative witness for Greenberger-Horne-Zeilinger entanglement
• Parametrization and optimization of Gaussian non-Markovian unravelings for open quantum dynamics
• Practical method to obtain a lower bound to the three-tangle
• Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement
• Multipartite Entanglement Evolution Under Separable Operations
• Quantifying entanglement of arbitrary-dimensional multipartite pure states in terms of the singular values of coefficient matrices
• Separable and Inseparable Quantum Trajectories
• Complete monogamy of the multipartite quantum mutual information
• Average entanglement dynamics in open two-qubit systems with continuous monitoring
• Complete Genuine Multipartite Entanglement Monotone
• Entanglement-assisted quantum speedup: Beating local quantum speed limits
• Equation of motion for multiqubit entanglement in multiple independent noisy channels
• Experimental verification of a coherence factorization law for quantum states
• Modeling and Deciphering on Two Spin-polariton Entanglement Experiments in NV Centers of Diamond
• Complete $k$-partite entanglement measure
• Symmetries of Multipartite Entanglement Evolution in Many-Sided Local Channels
• Tensor Networks for Entanglement Evolution
• Quantifying entanglement in multipartite conditional states of open quantum systems by measurements of their photonic environment