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The Gibbs free energy properties of a quantum {\it send, receive}communications system are studied. The communications model resembles theclassical Ising model of spins on a lattice in that the joint state of thequantum system is the product of sender and receiver states. However, thesystem differs from the classical case in that the sender and receiver spinstates are quantum superposition states coupled by a Hamiltonian operator. Abasic understanding of these states is directly relevant to communicationstheory and indirectly relevant to computation since the product states form abasis for entangled states. Highlights of the study include an exact method fordecimation for quantum spins. The main result is that the minimum Gibbs freeenergy of the quantum system in the product state is higher (lower capacity)than a classical system with the same parameter values. The result is bothsurprising and not. The channel characteristics of the quantum system in theproduct state are markedly inferior to those of the classical Ising system.Intuitively, it would seem that capacity should suffer as a result. Yet, onewould expect entangled states, built from product states, to have bettercorrelation properties.

Gibbs Free Energy Analysis of a Quantum Analog of the Classical Binary Symmetric Channel