Calculation of Mutual Information for Partially Coherent Gaussian Channels with Applications to Fiber Optics

The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive white Gaussian noise (AWGN) channel with various inputs show that, at high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the mixed terms. For the AWGN channel with a Gaussian input, analytical expressions are derived for high SNR. The decomposition method is applied to partially coherent channels and a property of such channels called "spectral loss" is developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be one effect that needs to be taken into account to explain the behavior of the capacity of nonlinear fiber-optic channels presented in recent studies.Comment: 30 pages, 9 figures, accepted for publication in IEEE Transactions on Information Theor

Theory of polarization and spatial information recovery by modal dispersal and phase conjugation

A general theory of polarization and spatial information recovery by modal dispersal and phase conjugation is presented by means of a coherency matrix formalism. The theory is applied to a system that consists of a multimode modal-scrambling fiber terminated by a conventional phase-conjugate mirror that reflects only one polarization component. The degree of polarization and the signal-to-noise ratio of the reconstructed field are discussed as a function of input-beam launching conditions. Some experimental results are also shown for comparison with the theory

Toward Photon-Efficient Key Distribution over Optical Channels

This work considers the distribution of a secret key over an optical (bosonic) channel in the regime of high photon efficiency, i.e., when the number of secret key bits generated per detected photon is high. While in principle the photon efficiency is unbounded, there is an inherent tradeoff between this efficiency and the key generation rate (with respect to the channel bandwidth). We derive asymptotic expressions for the optimal generation rates in the photon-efficient limit, and propose schemes that approach these limits up to certain approximations. The schemes are practical, in the sense that they use coherent or temporally-entangled optical states and direct photodetection, all of which are reasonably easy to realize in practice, in conjunction with off-the-shelf classical codes.Comment: In IEEE Transactions on Information Theory; same version except that labels are corrected for Schemes S-1, S-2, and S-3, which appear as S-3, S-4, and S-5 in the Transaction