The Sufficient Optimality Condition for Quantum Information Processing

The necessary and sufficient conditions of optimality of the decoding of quantum signals minimizing the Bayesian risk are generalized for the Shannon mutual information criteria. It is shown that for a linear channel with Gaussian boson noise these conditions are satisfied by coherent quasi-measurement of the canonical annihilation amplitudes in the received superposition. 1 Necessary and sufficient conditions of optimality In [5, 3] dealing with optimization of the reception of quantum signals such as electromagnetic waves in the optical band, the search for the necessary conditions of optimality in the class of randomized strategies based on indirect measurements was our main concern. According to this universal approach, we shall specify the randomized strategies by the operator probability measures Π(dβ) corresponding to quasi-measurements of certain noncommuting observables bj = ∫ βjΠ(dβ) such that Π(dβ) ≥ 0, ∫ Π(dβ) = 1̂. The equations derived in [5, 3] have the same form for both risk and information criteria of optimality: (R(β)− Λ)Π(dβ) = 0, Λ = ∫ R(β)Π(dβ), (1.1) Originally published in: Radio Eng. Electron. Phys., 19 (7), p. 39, 1974. [trans. from Radiotekhnika i Electronika, 1974, 19, 7, 1391–1395] 1