This page puts into perspective some of the more interesting results which I have obtained over the years.
Quantum Information
In a Hilbert space of dimension d, one can find (d+1) mutually unbiased bases if d is the power of a prime number. It has been conjectured that no more than three such bases exist for other dimensions.
- Strong numerical evidence has been provided that the conjecture holds in dimension d=6.
PT Symmetry
Some non-Hermitean Hamiltonians exhibit purely real spectra if they are invariant under simultaneous reversal of parity and time.
- Wigner's normal form of anti-unitary operators turns out to be a natural framework to describe the spectra of PT-symmetric operators.
Quantum State Reconstruction
The Pauli problem for a quantum particle is an early instance of the question which quantum state reconstruction later answers: do the probability distributions of position and momentum determine a unique pure state?
- I have obtained all pure states compatible with the two probability distributions and a third one, corresponding to a measurement along a slightly rotated postion axis...
Quantum Chaos and Integrability
It is often claimed that Schrödinger's equation as a linear equation cannot generate truly chaotic motion.
- The dynamics of the Configurational Quantum Cat Map is coincides with the dynamics of Arnold's classical Cat Map...
Other Results
- A theory which predicts the frequency shifts of an AFM cantilever immersed in a dense medium has been developed and tested experimentally.
- The Casimir
force increases when suitable squeezed
states of the electromagnetic field are excited.
- A useful method...
