Related papers: Universal Quantum Information Compression
We describe a universal information compression scheme that compresses any pure quantum i.i.d. source asymptotically to its von Neumann entropy, with no prior knowledge of the structure of the source. We introduce a diagonalisation…
The quantum entropy-typical subspace theory is specified. It is shown that any mixed state with von Neumann entropy less than h can be preserved approximately by the entropy-typical subspace with entropy= h. This result implies an universal…
A generic approach for compiling any classical block compression algorithm into a quantum block compression algorithm is presented. Using this technique, compression asymptoticaly approaching the von Neumann entropy of a qubit source can be…
A system of interacting qubits can be viewed as a non-i.i.d quantum information source. A possible model of such a source is provided by a quantum spin system, in which spin-1/2 particles located at sites of a lattice interact with each…
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…
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…
Data compression is a ubiquitous aspect of modern information technology, and the advent of quantum information raises the question of what types of compression are feasible for quantum data, where it is especially relevant given the…
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…
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 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…
Quantum state tomography--the practice of estimating a quantum state by performing measurements on it--is useful in a variety of contexts. We introduce "gentle tomography" as a version of tomography that preserves the measured quantum data.…
A model of a quantum information source is proposed, based on the Gibbs ensemble of ideal (free) particles (bosons or fermions). We identify the (thermodynamic) von Neumann entropy as the information rate and establish the classical…
Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate…
How much information about an unknown quantum state can be obtained by a measurement? We propose a model independent answer: the information obtained is equal to the minimum entropy of the outputs of the measurement, where the minimum is…
A classical random variable can be faithfully compressed into a sequence of bits with its expected length lies within one bit of Shannon entropy. We generalize this variable-length and faithful scenario to the general quantum source…
We consider the problem of optimal processing of quantum information at incomplete experimental data characterizing the quantum source. In particular, we then prove that for one-qubit quantum source the Jaynes principle offers a simple…
We present a formula that determines the optimal number of qubits per message that allows asymptotically faithful compression of the quantum information carried by an ensemble of mixed states. The set of mixed states determines a…
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 $H(rho_p)$, tend to 0. If…
Quantum information is defined by applying the concepts of ordinary (Shannon) information theory to a quantum sample space consisting of a single framework or consistent family. A classical analogy for a spin-half particle and other…
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…