[QIP-Sem] QIP seminar, Mon 5/18, 4:15, 36-428, Navascues,Miguel

[Peter Shor]

MIT Quantum Information Processing seminar
Monday 5/18 at 4:15 in 36-428
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 Navascues,Miguel (Imperial College London)

The power of symmetric extensions for entanglement detection

Abstract:

In this talk, I will analyze the speed of convergence of algorithms for entanglement detection based on PPT (Positive Partial Transpose) symmetric extensions, as conceived by Doherty et al. [1]. I will show that the states defined in [1] can be made separable just by partially depolarizing one of the parts. While the amount of necessary noise to induce separability on states that admit a plain N-symmetric extension decreases as O(1/N), the corresponding perturbation for states arising from PPT N-symmetric extensions decreases at least as O(1/N^2). I will use these results to estimate and compare the time and space complexity of both algorithms. Finally, I will consider the power of the PPT criterion alone: I will show how to derive upper bounds on the maximum possible distance between a PPT entangled state and the set of separable states by means of a simple construction.                     [1] A. C. Doherty, P. A. Parrilo and F. M. Spedalieri, Phys. Rev. A 69, 022308 (2004)
 
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