Conditional quantum channel and its certain construction

Horace P. Yuen

Communication theory problems incorporating quantum effects for optical-frequency applications are discussed. Under suitable conditions, a unique quantum channel model corresponding to a given classical space-time varying linear random channel is established. A procedure is described by which a proper density-operator representation applicable to any receiver configuration can be constructed directly from the channel output field. Some examples illustrating the application of our methods to the development of optical quantum channel representations are given. Optimizations of communication system performance under different criteria are considered. In particular, certain necessary and sufficient conditions on the optimal detector in M-ary quantum signal detection are derived. Some examples are presented. Parameter estimation and channel capacity are discussed briefly.

Zhihua Guo, Huaixin Cao

Robert Duran, Researcher, Robert Duran Iv, Independent

We formulate a constraint-based framework for quantum outcome realization in which realization is treated as a physical, observer-embedded process implemented by admissible quantum channels. Without modifying unitary dynamics or introducing collapse mechanisms, we impose minimal admissibility conditions—complete positivity, compositional closure, observer consistency, record accessibility, and variational selectability—on realization channels. Under these conditions, standard Born-rule measurement statistics are not postulated but are enforced as a necessary consequence of physical admissibility. We further show that multi-agent contradictions of the Frauchiger–Renner type are non-formulable, as the joint observer inferences required for such constructions cannot be jointly instantiated as admissible physical records within a single realization channel. Existing approaches to quantum measurement are thereby exhaustively classified according to whether they deny physical realization, avoid outcome selection, or admit physically selective realization subject to admissibility constraints. The framework does not advance a new interpretation of quantum mechanics; rather, it classifies the space of physically admissible realization mechanisms once outcome definiteness is assumed to be physical. Within this classification, probability assignment, global observer consistency, and the exclusion of certain paradoxical constructions follow as structural consequences rather than independent assumptions.

Masanori Ohya, Dėnes Petz, Noboru Watanabe

Dariusz Chruściński, Takashi Matsuoka

Anna Jenčová

We present a general theory of comparison of quantum channels, concerning with the question of simulability or approximate simulability of a given quantum channel by allowed transformations of another given channel. We introduce a modification of conditional min-entropies, with respect to the set F of allowed transformations, and show that under some conditions on F, these quantities characterize approximate simulability. If F is the set of free superchannels in a quantum resource theory of processes, the modified conditional min-entropies form a complete set of resource monotones. If the transformations in F consist of a preprocessing and a postprocessing of specified forms, approximate simulability is also characterized in terms of success probabilities in certain guessing games, where a preprocessing of a given form can be chosen and the measurements are restricted. These results are applied to several specific cases of simulability of quantum channels, including postprocessings, preprocessings and processing of bipartite channels by LOCC superchannels and by partial superchannels, as well as simulability of sets of quantum measurements. These questions are first studied in a general setting that is an extension of the framework of general probabilistic theories (GPT), suitable for dealing with channels. Here we prove a general theorem that shows that approximate simulability can be characterized by comparing outcome probabilities in certain tests. This result is inspired by the classical Le Cam randomization criterion for statistical experiments and contains its finite dimensional version as a special case.