相关论文: Quantum Kolmogorov complexity and its applications

We prove a strong Symmetry of Information relation for random strings (in the sense of Kolmogorov complexity) and establish tight bounds on the amount on nonuniformity that is necessary for extracting a string with randomness rate 1 from a…

Mutual information I in infinite sequences (and in their finite prefixes) is essential in theoretical analysis of many situations. Yet its right definition has been elusive for a long time. I address it by generalizing Kolmogorov Complexity…

The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…

Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. In this paper, we put forward a quantitative measure of coherence by following the axiomatic definition of coherence measures introduced…

According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative…

We survey various recent results that rigorously study the complexity of learning quantum states. These include progress on quantum tomography, learning physical quantum states, alternate learning models to tomography and learning classical…

The mutual information has been successfully used as a measure of correlation strength between quantum systems, especially for bipartite systems. Here we examine the use of this measure for multipartite quantum systems. For system of qubits…

While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…

Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…

This paper surveys the field of quantum communication complexity. Some interesting recent results are collected concerning relations to classical communication, lower bound methods, one-way communication, and applications of quantum…

An $n$-bit string is encoded as a sequence of non-orthogonal quantum states. The parity bit of that $n$-bit string is described by one of two density matrices, $\rho_0^{(n)}$ and $\rho_1^{(n)}$, both in a Hilbert space of dimension $2^n$.…

Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our…

We discuss a classical complexity of finite-dimensional unitary transformations, which can been seen as a computable approximation of classical descriptional complexity of a unitary transformation acting on a set of qubits.

We study quantum communication protocols, in which the players' storage starts out in a state where one qubit is in a pure state, and all other qubits are totally mixed (i.e. in a random state), and no other storage is available (for…

In this paper, we study quantum dense coding between two arbitrarily fixed particles in a (N+2)-particle maximally-entangled states through introducing an auxiliary qubit and carrying out local measurements. It is shown that the transmitted…

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…

This course of lectures has been taught for several years at the Lomonosov Moscow State University; its modified version in 2021 is read in the Zhejiang University (Hangzhou), in the framework of summer school on quantum computing. The…

In addition to the equations, physicists use the following additional difficult-to-formalize property: that the initial conditions and the value of the parameters must not be abnormal. We will describe a natural formalization of this…

We prove the first meta-complexity characterization of a quantum cryptographic primitive. We show that one-way puzzles exist if and only if there is some quantum samplable distribution of binary strings over which it is hard to approximate…

We discuss the quantum search algorithm using complex queries that has recently been published by Grover (quant-ph/9706005). We recall the algorithm adding some details showing which complex query has to be evaluated. Based on this version…