The extension of multiple-input multiple-output (MIMO) systems to the polarization domain is known to have potential benefits in terms of the spectral efficiency. It is thus of importance to understand how the channel influences the spectral efficiency, e.g., when a dual-polarized (DP) antenna setup should be favored over a single-polarized (SP) one. In this work, we study the achievable rate, i.e., the sum mutual information (MI) of all transmitted streams, over DP MIMO channels with linear receivers. We derive an approximation of the sum MI with a linear minimum mean squared error (LMMSE) or a zero forcing receiver which is an explicit function of statistical channel parameters. The evaluations of selected 4 × 4 SP and DP MIMO setups are based on channel measurements performed at 2.53 GHz in an urban macrocell scenario. The results reveal that DP antenna setups can yield substantial gains in the sum MI on links with high K-factors and high signal-to-noise ratios (SNRs). Moreover, the degradation in the sum MI with two streams due to the use of an LMMSE receiver is found to be small, especially for the DP antenna setup. The approximate evaluation of the sum MI is able to reproduce the SNR threshold region in which a second transmitted stream should be activated or one should switch from an SP to a DP antenna setup.

For a quantum (many-body) system with dynamical symmetry described by a given Lie group, we study the trace of exponential operators with complex coefficients in one of the irreducible subspaces in terms of the boson realization. By using this approach, for compact groups, we obtain the result of the trace that is consistent with the well-known Weyl character formula. For non-compact groups (with SU(1, 1) as an application), convergent condition of the trace is also obtained. This approach may be a powerful tool to study the thermodynamics of quantum (many-body) systems in equilibrium state or nonequilibrium processes.