Related papers: Quantum universal variable-length source coding

I introduce rate-distortion theory for quantum coding, and derive a lower bound, involving the coherent information, on the rate at which qubits must be used to encode a quantum source with a given maximum level of distortion per source…

Motivated from the fact that universal source coding on countably infinite alphabets is not feasible, this work introduces the notion of almost lossless source coding. Analog to the weak variable-length source coding problem studied by Han…

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 zero-error channel capacity is the maximum asymptotic rate that can be reached with error probability exactly zero, instead of a vanishing error probability. The nature of this problem, essentially combinatorial rather than…

In certain approaches to quantum computing the operations between qubits are non-deterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components;…

Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts---a randomness source and its readout. The source is…

Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…

We consider the maximum coding rate achievable by uniformly-random codes for the deletion channel. We prove an upper bound that's within 0.1 of the best known lower bounds for all values of the deletion probability $d,$ and much closer for…

Quantum random number generator harnesses the power of quantum mechanics to generate true random numbers, making it valuable for various scientific applications. However, real-world devices often suffer from imperfections that can undermine…

A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…

Secure random numbers are a fundamental element of many applications in science, statistics, cryptography and more in general in security protocols. We present a method that enables the generation of high-speed unpredictable random numbers…

In this paper we consider lossless source coding for a class of sources specified by the total variational distance ball centred at a fixed nominal probability distribution. The objective is to find a minimax average length source code,…

In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a…

We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…

We investigate the optimal estimation of quantum expectation value of a physical observable, which minimizes a mean error with respect to general measure of deviation, when a finite number of copies of a pure state are prepared. If pure…

The number of random bits required to approximate a target distribution in terms of un-normalized informational divergence is considered. It is shown that for a variable-to-variable length encoder, this number is lower bounded by the…

In this paper we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can…

In this work, lossy distributed compression of pairs of correlated sources is considered. Conventionally, Shannon's random coding arguments -- using randomly generated unstructured codebooks whose blocklength is taken to be asymptotically…

High-rate and large-distance quantum codes are expected to make fault-tolerant quantum computing more efficient, but most of them lack efficient fault-tolerant encoded-state preparation methods. We propose such a fault-tolerant encoder for…

Assuming an array that consists of two parallel lines of qubits and that permits only nearest neighbor interactions, we construct physical and logical circuitry to enable universal fault tolerant quantum computation under the [[7,1,3]]…