Matrix-element distributions as a signature of entanglement generation

  title={Matrix-element distributions as a signature of entanglement generation},
  author={Yaakov S. Weinstein and C. Stephen Hellberg},
  journal={Physical Review A},
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 multipartite entanglement. This occurs even when other statistical properties of the operators do not coincide with random matrices. Similarly, operators with some statistical properties of random matrices may not exhibit random matrix element distributions and will not produce states… Expand
Distribution of bipartite entanglement for random pure states
We calculate analytic expressions for the distribution of bipartite entanglement for pure random quantum states. All moments of the purity distribution are derived and an asymptotic expansion for theExpand
Entanglement and the speed of evolution of multi-partite quantum systems
There exists an interesting relationship between entanglement and the time evolution of composite quantum systems: quantum entanglement enhances the 'speed' of evolution of certain quantum states, asExpand
This work reviews and extends recent results concerning the distribution of entanglement, as well as nonlocality (in terms of inequality violations) in tripartite qubit systems. With recourse to aExpand
Multipartite Entanglement Generation in a Structured Environment
The results imply that the strong coupling between the harmonic oscillator and the N additional harmonic oscillators, and the large size of the additional oscillators will enhance non-Markovian dynamics and make it take a very long time for the entanglement to reach a stable value. Expand
Quantum pseudorandomness from cluster-state quantum computation
We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in theExpand
Multiqubit systems: highly entangled states and entanglement distribution
A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multiqubits states. In particular, our presentExpand
Parameters of pseudorandom quantum circuits
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parametersExpand
Nonlocality and entanglement in qubit systems
Nonlocality and quantum entanglement constitute two special aspects of the quantum correlations existing in quantum systems, which are of paramount importance in quantum-information theory.Expand
Quantum state transfer through a spin chain in two non-Markovian baths
The investigation takes one step toward practical quantum communication through a spin system where the two ends of the spin chain are independently immersed in two bosonic baths using the quantum state diffusion (QSD) equation approach. Expand
Global versus local quantum correlations in the Grover search algorithm
This work shall investigate how entanglement and nonlocality among register qubits vary as the Grover search algorithm is run, and encounter pronounced differences between the measures employed as far as bipartite and global correlations are concerned. Expand


Entanglement generation of nearly random operators.
This work studies the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way, including interpolating ensemble matrices, pseudorandom operators, and quantum chaotic evolution. Expand
Entangling power of the quantum baker's map
We investigate entanglement production in a class of quantum baker's maps. The dynamics of these maps is constructed using strings of qubits, providing a natural tensor-product structure forExpand
Testing statistical bounds on entanglement using quantum chaos.
An explicit statistical universal bound on entanglement is derived, which is also valid for the case of unequal dimensionality of the Hilbert spaces involved, and this describes well the bounds observed using composite quantized chaotic systems such as coupled tops. Expand
Pseudo-Random Unitary Operators for Quantum Information Processing
This work uses a nuclear magnetic resonance quantum processor to realize pseudorandom unitary operators that reproduce the expected random distribution of matrix elements and enables the practical application of random unitary operator in quantum communication and information processing protocols. Expand
Global entanglement in multiparticle systems
We define a polynomial measure of multiparticle entanglement which is scalable, i.e., which applies to any number of spin-12 particles. By evaluating it for three particle states, for eigenstates ofExpand
Interpolating ensembles of random unitary matrices.
  • Zyczkowski, Kus
  • Mathematics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
This work investigates transitions between ensembles of unitary random matrices modeling changes of statistical properties of quantum chaotic systems which are periodically time dependent and presents results concerning statistics of the quasi-energy levels and eigenvectors. Expand
Random unitary matrices
Methods of constructing random matrices typical of circular unitary and circular orthogonal ensembles are presented. We generate numerically random unitary matrices and show that the statisticalExpand
Signatures of chaos in the entanglement of two coupled quantum kicked tops.
  • P. Miller, S. Sarkar
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1999
It is found that the entanglement eventually increases linearly in time and the rate of this linear increase is itself a linear function of the sum of the positive Lyapunov exponents when averaged over initial points drawn from the classical distributions corresponding to the initial quantum product state. Expand
Saturation of the production of quantum entanglement between weakly coupled mapping systems in a strongly chaotic region.
It is elucidate that the increment of the nonlinear parameter of coupled kicked tops does not accelerate the entanglement production in the strongly chaotic region, and an approach to the dynamical inhibition ofEntanglement is suggested. Expand
Pseudorandom operators of the circular ensembles
We demonstrate quantum algorithms to implement pseudorandom operators that closely reproduce statistical properties of random matrices from the three universal classes: unitary, symmetric, andExpand