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Q: Quantenoptik und Photonik

Q 50: Quanteninformation IV

Q 50.3: Vortrag

Mittwoch, 15. März 2006, 14:30–14:45, HI

Non-negative discrete Wigner functions — •David Gross — Institute for Mathematical Science, Imperial College London, 48 Prince’s Gardens, London 2W7 2PE

We find that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set of unitary operations which preserve positivity. The result can be seen as a discrete version of Hudson’s Theorem. Hudson established that for continuous variable systems, the Wigner function of a pure state has no negative values if and only if the state is Gaussian. Turning to mixed states, it might be surmised that only convex combinations of stabilizer states give rise to non-negative Wigner distributions. We refute this conjecture by means of a counter-example.