Related papers: Quantum Kolmogorov Complexity
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
Diverse applications of Kolmogorov complexity to learning [CIKK16], circuit complexity [OPS19], cryptography [LP20], average-case complexity [Hir21], and proof search [Kra22] have been discovered in recent years. Since the running time of…
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…
We initiate the theory of communication complexity of individual inputs held by the agents, rather than worst-case or average-case. We consider total, partial, and partially correct protocols, one-way versus two-way, with and without help…
We provide tight upper and lower bounds on the expected minimum Kolmogorov complexity of binary classifiers that are consistent with labeled samples. The expected size is not more than complexity of the target concept plus the conditional…
Different observers do not have to agree on how they identify a quantum system. We explore a condition based on algorithmic complexity that allows a system to be described as an objective "element of reality". We also suggest an…
The complexity of the quantum state of a multiparticle system and the maximum possible accuracy of its quantum description are connected by a relation similar to the coordinate-momentum uncertainty relation. The coefficient in this relation…
This paper considers the realizability of quantum gates from the perspective of information complexity. Since the gate is a physical device that must be controlled classically, it is subject to random error. We define the complexity of gate…
There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of…
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…
Motivated by notions of quantum heuristics and by average-case rather than worst-case algorithmic analysis, we define quantum computational advantage in terms of individual problem instances. Inspired by the classical notions of Kolmogorov…
Kolmogorov complexity is often used as a convenient language for counting and/or probabilistic existence proofs. However, there are some applications where Kolmogorov complexity is used in a more subtle way. We provide one (somehow)…
Symmetry of information establishes a relation between the information that x has about y (denoted I(x : y)) and the information that y has about x (denoted I(y : x)). In classical information theory, the two are exactly equal, but in…
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
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…
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…
Krylov complexity has emerged as an important tool in the description of quantum information and, in particular, quantum chaos. Here we formulate Krylov complexity $K(t)$ for quantum mechanical systems as a path integral, and argue that at…
The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating a process of state preparation, transmission through the channel and subsequent measurement. It…
This article is a short review on the concept of information. We show the strong relation between Information Theory and Physics, beginning by the concept of bit and its representation with classical physical systems, and then going to the…