Information Gain in Quantum Communication Channels
In quantum communications the performances of an amplifier depend on the scheme of the channel in which the device is inserted. For example, both gain and noise figure of the amplifier depend on the kind of coding at the transmitter, and detection at the receiver.  In an optimized ideal channel, detection and coding are ideal, and both are “matched” on the same observable; the alphabet probability is optimized in order to satisfy the physical constraints on the line. In this case, the channel capacity is already achieved, and there is no need of amplification. However, when the channel is nonideal—either because of quantum mismatch between transmitter and receiver, because of losses along the line, or as a result of nonunit quantum efficiency at detectors—an appropriate amplification can improve the transmitted information, ideally achieving the channel capacity for infinite gain.
KeywordsMutual Information Master Equation Channel Capacity Wigner Function Noise Figure
Unable to display preview. Download preview PDF.
- C. W. Helstrom, Quantum Detection and Estimation Theory ( Academic Press, New York, 1976 ).Google Scholar
- For the description of quantum measurement probability in terms of “probability-operator-valued measure” (POM) see: M. Ozawa, J. M.th. Phys. 25, 79 (1984).Google Scholar
- E. B. Davies, Quantum theory of open systems, (Academic Press, London, New York, 1976 ).Google Scholar
- For the “completely positive instrument” description of quantum measurements see Ref. Google Scholar
- Essentially the POM comes from an orthogonal projection-valued measure that includes “probe” degrees of freedom of the apparatus, which are traced out to produce an outcome referring to the system alone.Google Scholar
- For evaluation of POM’s of ideal homodyne, double homodyne, and heterodyne detectors see: G. M. D’Ariano and M. G. A. Paris, Phys. Rev. A49, 3022 (1994); for the nonideal double homodyne detector see: U. Leonhardt and H. Paul, Phys. Rev. A 48, 4598 (1993).Google Scholar
- A. S. Holevo, Probl. Inf. Transm. 9, 177 (1973).Google Scholar
- Notice that here the Langevin equation has no noise term. However, this is unnecessary as long as the evolution of a POM is concerned.Google Scholar
- Actually, the quadrature channel is not perfectly optimized with respect to detection, because quadrature eigenstates have infinite energy. Thus, in principle, it might be possible to get R slightly lower than unit for this case.Google Scholar
- G. M. D’Ariano and C. Macchiavello, Phys. Rev. A 48 3947, (1993).Google Scholar
- H. M. Wiseman and G. J. Milburn, Phys. Rev. Lett. 70 548 (1993); Phys. Rev. A49 1350 (1994). For the adiabatic elimination see of the same authors: Phys. Rev. A47 642 (1994).Google Scholar