Related papers: Stationary quantum source coding
We define a large class of quantum sources and prove a quantum analog of the asymptotic equipartition property. Our proof relies on using local measurements on the quantum source to obtain an associated classical source. The classical…
Noiseless coding theorem for finite stationary memoryless information sources is proved by using induction on the number of source symbols and the inequality of geometric and harmonic means.
We report an experimental demonstration of Schumacher's quantum noiseless coding theorem. Our experiment employs a sequence of single photons each of which represents three qubits. We initially prepare each photon in one of a set of 8…
For a real number $r>0$, let $F(r)$ be the family of all stationary ergodic quantum sources with von Neumann entropy rates less than $r$. We prove that, for any $r>0$, there exists a blind, source-independent block compression scheme which…
We study source compression with a helper in the fully quantum regime, extending our earlier result on classical source compression with a quantum helper [arXiv:1501.04366, 2015]. We characterise the quantum resources involved in this…
We present a proof for the quantum channel coding theorem which relies on the fact that a randomly chosen code space typically is highly suitable for quantum error correction. In this sense, the proof is close to Shannon's original…
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…
The general scheme of data compression using the quantum noiseless coding theorem of Schumacher is dicussed for general quantum sources. When the Hilbert space of the quantum source is decomposable into orthogonal subspaces, one can first…
A coding theorem is proved for a class of stationary channels with feedback in which the output Y_n = f(X_{n-m}^n, Z_{n-m}^n) is the function of the current and past m symbols from the channel input X_n and the stationary ergodic channel…
We consider ergodic causal classical-quantum channels (cq-channels) which additionally have a decaying input memory. In the first part we develop some structural properties of ergodic cq-channels and provide equivalent conditions for…
The weak converse coding theorems have been proved for the quantum source and channel. The results give the lower bound for capacity of source and the upper bound for capacity of channel. The monotonicity of mutual quantum information have…
Shanon's fundamental coding theorems relate classical information theory to thermodynamics. More recent theoretical work has been successful in relating quantum information theory to thermodynamics. For example, Schumacher proved a quantum…
We extend the data compression theorem to the case of ergodic quantum information sources. Moreover, we provide an asymptotically optimal compression scheme which is based on the concept of high probability subspaces. The rate of this…
The Parity Source Coder is a protocol for data compression which is based on a set of parity checks organized in a sparse random network. We consider here the case of memoryless unbiased binary sources. We show that the theoretical capacity…
The simplest example of a quantum information source with memory is a mixed source which emits signals entirely from one of two memoryless quantum sources with given a priori probabilities. Considering a mixed source consisting of a general…
It is demonstrated how to represent asymptotically mean stationary (AMS) random sources with values in standard spaces as mixtures of ergodic AMS sources. This an extension of the well known decomposition of stationary sources which has…
Consider a source E of pure quantum states with von Neumann entropy S. By the quantum source coding theorem, arbitrarily long strings of signals may be encoded asymptotically into S qubits/signal (the Schumacher limit) in such a way that…
We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…
The information spectrum approach gives general formulae for optimal rates of various information theoretic protocols, under minimal assumptions on the nature of the sources, channels and entanglement resources involved. This paper…
We consider transmission of stationary and ergodic sources over non-ergodic composite channels with channel state information at the receiver (CSIR). Previously we introduced alternate capacity definitions to Shannon capacity, including the…