Related papers: Quantum Algorithmic Entropy
By considering matter as a constraint on the availability of gravitational degrees of freedom and accounting for the statistical interpretation of Rindler horizons, the freedom to construct quantum gravity theories reproducing General…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's…
It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori…
Regarding the strange properties of quantum entropy and entanglement, e.g., the negative quantum conditional entropy, we revisited the foundations of quantum entropy, namely, von Neumann entropy, and raised the new method of quantum…
We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the $G_N\rightarrow 0$ limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we…
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…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
The underlying probabilistic theory for quantum mechanics is non-Kolmogorovian. The order in which physical observables will be important if they are incompatible (non-commuting). In particular, the notion of conditioning needs to be…
In this paper, we review the concept of entropy in connection with the description of quantum unstable systems. We revise the conventional definition of entropy due to Boltzmann and extend it so as to include the presence of complex-energy…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
The area law for entanglement entropy fundamentally reflects the complexity of quantum many-body systems, demonstrating ground states of local Hamiltonians to be represented with low computational complexity. While this principle is…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
We define a quantum entropy conditioned on post-selection which has the von Neumann entropy of pure states as a special case. This conditional entropy can take negative values which is consistent with part of a quantum system containing…
Instead of static entropy we assert that the Kolmogorov complexity of a static structure such as a solid is the proper measure of disorder (or chaoticity). A static structure in a surrounding perfectly-random universe acts as an interfering…
This paper investigates the relationship between categorical entropy and von Neumann entropy of quantum lattices. We begin by studying the von Neumann entropy, proving that the average von Neumann entropy per site converges to the logarithm…
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about…
Given a reference computer, Kolmogorov complexity is a well defined function on all binary strings. In the standard approach, however, only the asymptotic properties of such functions are considered because they do not depend on the…
Quantum Field Theory (QFT) represents a vast generalization of Quantum Mechanics (QM), as it deals with systems that have an infinite number of degrees of freedom. The Stone-von Neumann theorem, which establishes the equivalence of…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…