Browsing División de Nanociencias y Materiales by Author "Planat, Michel"

Now showing items 1-7 of 7

    • A survey of finite algebraic geometrical structures underlying mutually unbiased quantum measurements 

      Planat, Michel; Rosu Barbus, Haret-Codratian; Perrine, Serge (2006)
      "The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are reviewed and an emerging link between them is outlined. It is shown that these methods employ ...

    • Cyclotomy and Ramanujan sums in quantum phase locking 

      Planat, Michel; Rosu Barbus, Haret-Codratian (2003)
      "Phase-locking governs the phase noise in classical clocks through effects described in precise mathematical terms. We seek here a quantum counterpart of these effects by working in a finite Hilbert space. We use a coprimality ...

    • Mutually unbiased bases and finite projective planes 

      Saniga, Metod; Planat, Michel; Rosu Barbus, Haret-Codratian (2004)
      "It is conjectured that the question of the existence of a set of d+1 mutually unbiased bases in a d-dimensional Hilbert space if d differs from a power of a prime number is intimately linked with the problem of whether ...

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

      Planat, Michel; Rosu Barbus, Haret-Codratian (2005)
      "Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is a constant equal to 1/d?, with d the dimension of the finite Hilbert space, are becoming more and ...

    • On arithmetic detection of grey pulses with application to Hawking radiation 

      Rosu Barbus, Haret-Codratian; Planat, Michel (2002)
      "Micron-sized black holes do not necessarily have a constant horizon temperature distribution. The black hole remote-sensing problem means to find out the "surface" temperature distribution of a small black hole from the ...

    • Ramanujan sums for signal processing of low-frequency noise 

      Planat, Michel; Rosu Barbus, Haret-Codratian; Perrine, Serge (2002)
      "An aperiodic (low-frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Mobius function or Mangoldt function, which are coding sequences for prime numbers. In the ...

    • The hyperbolic, the arithmetic and the quantum phase 

      Saniga, Metod; Planat, Michel; Rosu Barbus, Haret-Codratian (2004)
      "We develop a new approach of the quantum phase in an Hilbert space of finite dimension which is based on the relation between the physical concept of phase locking and mathematical concepts such as cyclotomy and the ...