Related papers: Optimality in Quantum Data Compression using Dynam…
B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide…
Consider a general quantum stochastic source that emits at discrete time steps quantum pure states which are chosen from a finite alphabet according to some probability distribution which may depend on the whole history. Also, fix two…
We consider the most general (finite-dimensional) quantum mechanical information source, which is given by a quantum system $A$ that is correlated with a reference system $R$. The task is to compress $A$ in such a way as to reproduce the…
Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum R\'enyi entropies. In order to do this, we appeal to a very general quantum encoding scheme that…
Ask how the quantum compression of ensembles of pure states is affected by the availability of entanglement, and in settings where the encoder has access to side information. We find the optimal asymptotic quantum rate and the optimal…
By looking at quantum data compression in the second quantisation, we present a new model for the efficient generation and use of variable length codes. In this picture lossless data compression can be seen as the {\em minimum energy}…
We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length…
We study compression strategies for multipartite entanglement distribution under uncertainty in the partitioning of the quantum state. When the partition is not known at the time of state preparation, we show that a joint design of the…
In order to compress quantum messages without loss of information it is necessary to allow the length of the encoded messages to vary. We develop a general framework for variable-length quantum messages in close analogy to the classical…
We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops…
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 the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of…
The emerging field of quantum machine learning has the potential of revolutionizing our perspectives of quantum computing and artificial intelligence. In the predominantly empirical realm of quantum machine learning, a theoretical void…
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…
This paper proposes a novel entropy encoding technique for lossless data compression. Representing a message string by its lexicographic index in the permutations of its symbols results in a compressed version matching Shannon entropy of…
This work introduces the Schmidt quantum compressor, an innovative approach to quantum data compression that leverages the principles of Schmidt decomposition to encode quantum information efficiently. In contrast to traditional variational…
We provide a rate distortion interpretation of the problem of quantum data compression of ensembles of mixed states with commuting density operators. There are two versions of this problem. In the visible case the sequence of states is…
We introduce a universal quantization scheme based on random coding, and we analyze its performance. This scheme consists of a source-independent random codebook (typically_mismatched_ to the source distribution), followed by optimal…
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…
Quantum information theory, particularly its entropic formulations, has made remarkable strides in characterizing quantum systems and tasks. However, a critical dimension remains underexplored: computational efficiency. While classical…