Related papers: Universal Compression of Ergodic Quantum Sources
This paper is a continuation of Poiret-Robert-Thomann (2013) where we studied a randomisation method based on the Laplacian with harmonic potential. Here we extend our previous results to the case of any polynomial and confining potential…
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…
It is shown that an i.i.d. binary source sequence $X_1, \ldots, X_n$ can be losslessly compressed at any rate above entropy such that the individual decoding of any $X_i$ reveals \emph{no} information about the other bits $\{X_j : j \neq…
The general stable quantum memory unit is a hybrid consisting of a classical digit with a quantum digit (qudit) assigned to each classical state. The shape of the memory is the vector of sizes of these qudits, which may differ. We determine…
As it is known, universal codes, which estimate the entropy rate consistently, exist for stationary ergodic sources over finite alphabets but not over countably infinite ones. We generalize universal coding as the problem of universal…
Based on the concept of many-letter theory, an observable is defined measuring the raw quantum information content of single messages. A general characterization of quantum codes using the Kraus representation is given. Compression codes…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
This short note proves that a Laplacian cannot be quantum uniquely ergodic if it possesses a quasimode of order zero which (i) has a singular limit, and (ii) is a linear combination of a uniformly bounded number of eigenfunctions (modulo an…
We introduce a model of non-unitary quantum dynamics that exhibits infinitely long-lived discrete spatiotemporal order robust against any unitary or dissipative perturbation. Ergodicity is evaded by combining a sequence of projective…
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…
In this paper, we consider the one-shot version of the classical Wyner-Ziv problem where a source is compressed in a lossy fashion when only the decoder has access to a correlated side information. Following the entropy-constrained…
By employing at recent proposal (R. Filip, P. Marek and U.L. Andersen, Phys. Rev. A {\bf 71}, 042308 (2005) \cite{Filip05.pra}), we experimentally demonstrate a universal, deterministic and high-fidelity squeezing transformation of an…
We discuss the quantitative ergodicity of quantum Markov semigroups in terms of the trace distance from the stationary state, providing a general criterion based on the spectral decomposition of the Lindblad generator. We then apply this…
We consider the problem of joint universal variable-rate lossy coding and identification for parametric classes of stationary $\beta$-mixing sources with general (Polish) alphabets. Compression performance is measured in terms of…
We prove that quantum expander codes can be combined with quantum fault-tolerance techniques to achieve constant overhead: the ratio between the total number of physical qubits required for a quantum computation with faulty hardware and the…
We demonstrate the onset of strong on-site localization in a one-dimensional many-particle system. The localization is obtained by constructing, in an explicit form, a bounded sequence of on-site energies that eliminates resonant hopping…
We investigate entropy transport for universal scaling phenomena in closed quantum many-body systems far from equilibrium. From spatially resolved experimental data of a spinor Bose gas, we demonstrate that entropy decreases on…
We prove that the quantum relative entropy decreases monotonically under the application of any positive trace-preserving linear map, for underlying separable Hilbert spaces. This answers in the affirmative a natural question that has been…
This paper considers the problem of data compression for dependent quantum systems. It is the second in a series under the same title. As in the previous paper, we are interested in Lempel--Ziv encoding for quantum Gibbs ensembles. Here, we…
Quantum systems with more than two levels $-$ so-called qudits $-$ offer increased computational density and reduced circuit complexity compared to qubit-based architectures, but achieving universal and scalable control remains challenging.…