Mutually unbiased phase states, phase uncertainties, and Gauss sums

Details Mutually unbiased phase states, phase uncertainties, and Gauss sums Mutually unbiased phase states, phase uncertainties, and Gauss sums

2005-06-16

arxiv.org/abs/quant-ph/0506128v3

Eur. Phys. J. D 36, 133-139 (Oct. 2005)

Physics

Quantum Physics

16 pages, a few typos corrected, some references updated, note acknowledging I. Shparlinski added

Scientific paper

10.1140/epjd/e2005-00208-4

Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is a constant equal to 1/sqrt{d), with d the dimension of the finite Hilbert space, are becoming more and more studied for applications such as quantum tomography and cryptography, and in relation to entangled states and to the Heisenberg-Weil group of quantum optics. Complete sets of MUBs of cardinality d+1 have been derived for prime power dimensions d=p^m using the tools of abstract algebra. Presumably, for non prime dimensions the cardinality is much less. Here we reinterpret MUBs as quantum phase states, i.e. as eigenvectors of Hermitean phase operators generalizing those introduced by Pegg & Barnett in 1989. We relate MUB states to additive characters of Galois fields (in odd characteristic p) and to Galois rings (in characteristic 2). Quantum Fourier transforms of the components in vectors of the bases define a more general class of MUBs with multiplicative characters and additive ones altogether. We investigate the complementary properties of the above phase operator with respect to the number operator. We also study the phase probability distribution and variance for general pure quantum electromagnetic states and find them to be related to the Gauss sums, which are sums over all elements of the field (or of the ring) of the product of multiplicative and additive characters. Finally, we relate the concepts of mutual unbiasedness and maximal entanglement. This allows to use well studied algebraic concepts as efficient tools in the study of entanglement and its information aspects

Affiliated with

Also associated with

No associations

Rating

Mutually unbiased phase states, phase uncertainties, and Gauss sums does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mutually unbiased phase states, phase uncertainties, and Gauss sums, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mutually unbiased phase states, phase uncertainties, and Gauss sums will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-5378