dorsal/arxiv
View SchemaEmergence of typical entanglement in two-party random processes
| Authors | O. C. O. Dahlsten, R. Oliveira, M. B. Plenio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701125 |
| URL | https://arxiv.org/abs/quant-ph/0701125 |
| DOI | 10.1088/1751-8113/40/28/S16 |
| Journal | J. Phys. A: Math. Theor. 40 (2007) 8081-8108 |
Abstract
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 previous work we proved that the maximal entanglement is reached to a fixed arbitrary accuracy within $O(N^3)$ steps, where $N$ is the total number of qubits. Here we provide a detailed and more pedagogical proof. We demonstrate that one can use the so-called stabilizer gates to simulate this process efficiently on a classical computer. Furthermore, we discuss three ways of identifying the transition from the phase of rapid spread of entanglement to the stationary phase: (i) the time when saturation of the maximal entanglement is achieved, (ii) the cut-off moment, when the entanglement probability distribution is practically stationary, and (iii) the moment block entanglement scales exhibits volume scaling. We furthermore investigate the mixed state and multipartite setting. Numerically we find that classical and quantum correlations appear to behave similarly and that there is a well-behaved phase-space flow of entanglement properties towards an equilibrium, We describe how the emergence of typical entanglement can be used to create a much simpler tripartite entanglement description. The results form a bridge between certain abstract results concerning typical (also known as generic) entanglement relative to an unbiased distribution on pure states and the more physical picture of distributions emerging from random local interactions.
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"abstract": "We investigate the entanglement within a system undergoing a random, local\nprocess. We find that there is initially a phase of very fast generation and\nspread of entanglement. At the end of this phase the entanglement is typically\nmaximal. In previous work we proved that the maximal entanglement is reached to\na fixed arbitrary accuracy within $O(N^3)$ steps, where $N$ is the total number\nof qubits. Here we provide a detailed and more pedagogical proof. We\ndemonstrate that one can use the so-called stabilizer gates to simulate this\nprocess efficiently on a classical computer. Furthermore, we discuss three ways\nof identifying the transition from the phase of rapid spread of entanglement to\nthe stationary phase: (i) the time when saturation of the maximal entanglement\nis achieved, (ii) the cut-off moment, when the entanglement probability\ndistribution is practically stationary, and (iii) the moment block entanglement\nscales exhibits volume scaling. We furthermore investigate the mixed state and\nmultipartite setting. Numerically we find that classical and quantum\ncorrelations appear to behave similarly and that there is a well-behaved\nphase-space flow of entanglement properties towards an equilibrium, We describe\nhow the emergence of typical entanglement can be used to create a much simpler\ntripartite entanglement description. The results form a bridge between certain\nabstract results concerning typical (also known as generic) entanglement\nrelative to an unbiased distribution on pure states and the more physical\npicture of distributions emerging from random local interactions.",
"arxiv_id": "quant-ph/0701125",
"authors": [
"O. C. O. Dahlsten",
"R. Oliveira",
"M. B. Plenio"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1751-8113/40/28/S16",
"journal_ref": "J. Phys. A: Math. Theor. 40 (2007) 8081-8108",
"title": "Emergence of typical entanglement in two-party random processes",
"url": "https://arxiv.org/abs/quant-ph/0701125"
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