Related papers: Quantum universal variable-length source coding
We present a probabilistic quantum processor for qudits. The processor itself is represented by a fixed array of gates. The input of the processor consists of two registers. In the program register the set of instructions (program) is…
Continuous-Variable (CV) devices are a promising platform for demonstrating large-scale quantum information protocols. In this framework, we define a general quantum computational model based on a CV hardware. It consists of vacuum input…
Consider a sequence $X^n$ of length $n$ emitted by a Discrete Memoryless Source (DMS) with unknown distribution $p_X$. The objective is to construct a lossless source code that maps $X^n$ to a sequence $\widehat{Y}^m$ of length $m$ that is…
Unitary $t$-designs are the bread and butter of quantum information theory and beyond. An important issue in practice is that of efficiently constructing good approximations of such unitary $t$-designs. Building on results by Aubrun (Comm.…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
We determine the optimal rates of universal quantum codes for entanglement transmission and generation under channel uncertainty. In the simplest scenario the sender and receiver are provided merely with the information that the channel…
We establish a theory of quantum-to-classical rate distortion coding. In this setting, a sender Alice has many copies of a quantum information source. Her goal is to transmit classical information about the source, obtained by performing a…
A universal programmable discriminator can perform the discrimination between two unknown states, and the optimal solution can be approached via the discrimination between the two averages over the uniformly distributed unknown input pure…
Universal fixed-to-variable lossless source coding for memoryless sources is studied in the finite blocklength and higher-order asymptotics regimes. Optimal third-order coding rates are derived for general fixed-to-variable codes and for…
In this paper, we consider the problem of constructing optimal average-length binary codes under the constraint that each codeword must contain at most $D$ ones, where $D$ is a given input parameter. We provide an $O(n^2D)$-time complexity…
In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices…
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…
The class of incoherent operations induces a pre-order on the set of quantum pure states, defined by the possibility of converting one state into the other by transformations within the class. We prove that if two $n$-dimensional pure…
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
Medium-scale quantum devices that integrate about hundreds of physical qubits are likely to be developed in the near future. However, such devices will lack the resources for realizing quantum fault tolerance. Therefore, the main challenge…
This paper shows that the normalized maximum likelihood~(NML) code-length calculated in [1] is an upper bound on the NML code-length strictly calculated for the Gaussian Mixture Model. When we use this upper bound on the NML code-length, we…
In this paper we study von Neumann un-biasing normalisation for ideal and real quantum random number generators, operating on finite strings or infinite bit sequences. In the ideal cases one can obtain the desired un-biasing. This relies…
A general theory of quantum error avoiding codes is established, and new light is shed on the relation between quantum error avoiding and correcting codes. Quantum error avoiding codes are found to be a special type of highly degenerate…
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…
Quantum computers promise to transform our notions of computation by offering a completely new paradigm. To achieve scalable quantum computation, optimizing compilers and a corresponding software design flow will be essential. We present a…