The emergence of typical entanglement in two-party random processes

@article{Dahlsten2007TheEO,
  title={The emergence of typical entanglement in two-party random processes},
  author={Oscar C. O. Dahlsten and R. Oliveira and Martin Bodo Plenio},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2007},
  volume={40},
  pages={8081 - 8108}
}
We investigate the entanglement within a system undergoing a random, local process. We find that there is initially a phase of very fast generation and spread of entanglement. At the end of this phase the entanglement is typically maximal. In Oliveira et al (2007 Phys. Rev. Lett. 98 130502) we proved that the maximal entanglement is reached to a fixed arbitrary accuracy within O(N3) steps, where N is the total number of qubits. Here we provide a detailed and more pedagogical proof. We… 
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References

SHOWING 1-10 OF 76 REFERENCES
Aspects of Generic Entanglement
We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the ``concentration
Optimal Superdense Coding of Entangled States
TLDR
A one-shot method for preparing pure entangled states between a sender and a receiver at a minimal cost of entanglement and quantum communication and a direct proof of the achievability of the optimal superdense coding protocol for entangled states produced by a memoryless source.
Entanglement-area law for general bosonic harmonic lattice systems (14 pages)
We demonstrate that the entropy of entanglement and the distillable entanglement of regions with respect to the rest of a general harmonic-lattice system in the ground or a thermal state scale at
ENTANGLEMENT AND DECOHERENCE IN SPIN GASES
We study the dynamics of entanglement in spin gases. A spin gas consists of a (large) number of interacting particles whose random motion is described classically while their internal degrees of
Reversibility of Local Transformations of Multiparticle Entanglement
TLDR
It is shown that, for any reversible transformation, the relative entropy of entanglement for any two parties must remain constant, and there is true three-party non-locality (i.e. not all three party entangled states is equivalent to two-party entangling).
Canonical and micro-canonical typical entanglement of continuous variable systems
We present a framework, compliant with the general canonical principle of statistical mechanics, to define measures on the set of pure Gaussian states of continuous variable systems. Within such a
Typical entanglement of stabilizer states
How entangled is a randomly chosen bipartite stabilizer state? We show that if the number of qubits each party holds is large, the state will be close to maximally entangled with probability
Teleportation Fidelities of Squeezed States from Thermodynamical State Space Measures
We introduce a ''microcanonical'' measure (complying with the ''general canonical principle'') over the second moments of pure bosonic Gaussian states under an energy constraint. We determine the
Quantum, classical, and total amount of correlations in a quantum state (11 pages)
We give an operational definition of the quantum, classical, and total amounts of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work
Entanglement and the foundations of statistical mechanics
Statistical mechanics is one of the most successful areas of physics. Yet, almost 150 years since its inception, its foundations and basic postulates are still the subject of debate. Here we suggest
...
...