Matrix Element Distribution as a Signature of Entanglement Generation

Abstract

We explore connections between an operator's matrix element distribution and its entanglement generation. Operators with matrix element distributions similar to those of random matrices generate states of high multi-partite entanglement. This occurs even when other statistical properties of the operators do not conincide with random matrices. Similarly, operators with some statistical properties of random matrices may not exhibit random matrix element distributions and will not produce states with high levels of multi-partite entanglement. Finally, we show that operators with similar matrix element distributions generate similar amounts of entanglement.

7 pages, 6 figures, to be published PRA, partially supersedes quant-ph/0405053, expands quant-ph/0502110

References in corpus (20)

• Global entanglement in multiparticle systems
• Randomizing quantum states: Constructions and applications
• Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
• Entanglement as a signature of quantum chaos
• Superdense coding of quantum states
• Testing statistical bounds on entanglement using quantum chaos
• Entangling power of quantized chaotic systems
• Remote preparation of quantum states
• Dynamical aspects of quantum entanglement for weakly coupled kicked tops
• Entangling power of the quantum baker's map
• Entanglement production in coupled chaotic systems : Case of the Kicked Tops
• Efficient Quantum Computing of Complex Dynamics
• Semiclassical time-evolution of the reduced density matrix and dynamically assisted generation of entanglement for bipartite quantum systems
• Saturation of the production of quantum entanglement between weakly coupled mapping systems in strongly chaotic region
• Global entangling properties of the coupled kicked tops
• Entanglement Generation of Nearly-Random Operators
• Dephasing in a quantum pump
• Search for two-scale localization in disordered wires in a magnetic field
• Quantum Cellular Automata Pseudo-Random Maps
• Pseudo-random operators of the circular ensembles

Cited by in corpus (10)

• Multi-Qubit Systems: Highly Entangled States and Entanglement Distribution
• Nonlocality and entanglement in the XY model
• Nonlocality and entanglement in qubit systems
• Anticoncentration theorems for schemes showing a quantum speedup
• Distribution of bipartite entanglement for random pure states
• Parameters of Pseudo-Random Quantum Circuits
• Optimized design of universal two-qubit gates
• Quantum pseudo-randomness from cluster-state quantum computation
• Generalized Entanglement as a Natural Framework for Exploring Quantum Chaos
• Entangling power of baker's map: Role of symmetries