Related papers: Complexity-constrained quantum thermodynamics
The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to noisy quantum operations. Here, we establish a remainder term…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
Landauer's Principle that information loss from a computation implies entropy increase can be rigorously proved from mathematical physics. However, carefully examining its detailed formulation reveals that the traditional identification of…
There are at least a number of ways to formally define complexity. Most of them relate to some kind of minimal description of the studied object. Being this one in form of minimal resources of minimal effort needed to generate the object…
We show that information in quantum memory can be erased and recovered perfectly if it is necessary. That the final states of environment are completely determined by the initial states of the system allows that an easure operation can be…
In classical information theory, entropy rate and Kolmogorov complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of…
By establishing a relation between information erasure and continuous phase transitions we generalise the Landauer bound to analog computing systems. The entropy production per degree of freedom during erasure of an analog variable (reset…
In spite of many results in quantum information theory, the complex nature of compound systems is far from being clear. In general the information is a mixture of local, and non-local ("quantum") information. To make this point more clear,…
For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
In practice, qubit reset must be operated in an extremely short time, which incurs a thermodynamic cost within multiple orders of magnitude above the Landauer bound. We present a general framework to determine the minimal thermodynamic cost…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
In this paper we give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the…
Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In…
Ubiquitous in quantum computing is the step to encode data into a quantum state. This process is called quantum state preparation, and its complexity for non-structured data is exponential on the number of qubits. Several works address this…
In recent years we have witnessed a concentrated effort to make sense of thermodynamics for small-scale systems. One of the main difficulties is to capture a suitable notion of work that models realistically the purpose of quantum machines,…
We formulate a minimal model of a quantum particle detector as an autonomous quantum thermal machine. Our goal is to establish how entropy production, which is needed to maintain the detector out of equilibrium, is linked to the quality of…
Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known…
We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size,…