We have constructed universal codes for quantum lossless source coding and classical-quantum channel coding. In this construction, we essentially employ group representation theory. In order to treat quantum lossless source coding, universal approximation of multi-copy states is discussed in terms of the quantum relative entropy.
We simply construct a quantum universal variable-length source code in which, independent of information source, both of the average error and the probability that the coding rate is greater than the entropy rate H(rhop), tend to 0. If H(rhop) is estimated, we can compress the coding rate to the admissible rate H(rhop) with a probability close to 1. However, when we perform a naive measurement for the estimation of H(rhop), the input state is demolished. By smearing the measurement, we successfully treat the trade-off between the estimation of H(rhop) and the non-demolition of the input state. Our protocol can be used not only for the Schumacher's scheme but also for the compression of entangled states.
We simply construct a quantum universal variable-length source code in which, independent of information source, both of the average error and the probability that the coding rate is greater than the entropy rate H(\overline{\rho}_p), tend to 0. If H(\overline{\rho}_p) is estimated, we can compress the coding rate to the admissible rate H(\overline{\rho}_p) with a probability close to 1. However, when we perform a naive measurement for the estimation of H(\overline{\rho}_p), the input state is demolished. By smearing the measurement, we successfully treat the trade-off between the estimation of H(\overline{\rho}_p) and the non-demolition of the input state. Our protocol can be used not only for the Schumacher's scheme but also for the compression of entangled states.
Coding theorems and (strong) converses for memoryless quantum communication channels and quantum sources are proved: for the quantum source the coding theorem is reviewed, and the strong converse proven. For classical information transmission via quantum channels we give a new proof of the coding theorem, and prove the strong converse, even under the extended model of nonstationary channels. As a by-product we obtain a new proof of the famous Holevo bound. Then multi-user systems are investigated, and the capacity region for the quantum multiple access channel is determined. The last chapter contains a preliminary discussion of some models of compression of correlated quantum sources, and a proposal for a program to obtain operational meaning for quantum conditional entropy. An appendix features the introduction of a notation and calculus of entropy in quantum systems.
Constructing optimal quantum information protocols without complete knowledge of the underlying states or channels is a central challenge. We address this challenge by developing universal correlation detection as a common building block for quantum communication. Our detectors distinguish a bipartite state from the product of its marginals and attain the same first-order asymptotic performance as optimal tests constructed with complete state information. For general bipartite quantum states, knowledge of a single marginal suffices: a detector depending only on that marginal is first-order optimal for every compatible state. For classical-quantum states, the detector is fully universal and requires no prior state information. By combining these detectors with position-based decoding and convex splitting, we construct channel-independent coding schemes that achieve capacity for a range of communication tasks. These results turn universal correlation detection into a systematic tool for universal protocol design, providing a unified route to designing capacity-achieving protocols for many communication tasks over unknown quantum channels.