Related papers: Entropy of a quantum channel
Entropy production is the crucial quantity characterizing irreversible phenomena and the second law of thermodynamics. Yet, a ubiquitous definition eludes consensus. Given that entropy production arises from incomplete access to…
We investigate the basic theoretical issues in the quantum entanglement of particle pairs created from the vacuum in a time-dependent background field or spacetime. Similar to entropy generation from these processes which depends on the…
The main topic of this thesis is the proof of two fundamental entropic inequalities for quantum Gaussian channels. Quantum Gaussian channels model the propagation of electromagnetic waves through optical fibers and free space in the quantum…
Coherence is a basic notion for quantum states. Instead of quantum states, in this work, We establish a resource theory for quantifying the coherence of Gaussian channels. To do this, we propose the definitions of incoherent Gaussian…
The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of…
The von Neumann entropy for an electron in periodic, disorder and quasiperiodic quantum small-world networks(QSWNs) are studied numerically. For the disorder QSWNs, the derivative of the spectrum averaged von Neumann entropy is maximal at a…
We establish a tight upper bound for the difference in von Neumann entropies between two quantum states, $\rho_1$ and $\rho_2$. This bound is expressed in terms of the von Neumann entropies of the mutually orthogonal states derived from the…
Entanglement is a key issue in the quantum physics which gives rise to resources for achieving tasks that are not possible within the realm of classical physics. Quantum entanglement varies with the evolution of the quantum systems. It is…
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…
Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…
State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under…
One of the most counterintuitive aspects of quantum theory is its claim that there is 'intrinsic' randomness in the physical world. Quantum information science has greatly progressed in the study of intrinsic, or secret, quantum randomness…
The paper examines and critiques the expression of entropy as the logarithm of the number of quantum states of a physical system. Boltzmann method of expressing entropy as the logarithm of the number of states of a gas with a given total…
For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum…
The content of phase information of an arbitrary phase--sensitive measurement is evaluated using the maximum likelihood estimation. The phase distribution is characterized by the relative entropy--a nonlinear functional of input quantum…
We present a noncommutative optimal transport framework for quantum channels acting on von Neumann algebras. Our central object is the Lipschitz cost measure, a transportation-inspired quantity that evaluates the minimal cost required to…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
We explore the thermodynamics of quantum processes (quantum channels) by axiomatically introducing the free energy for channels, defined via the quantum relative entropy with an absolutely thermal channel whose fixed output is in…
Quantum capacity, as the ultimate transmission rate of quantum communication, is characterized by regularized coherent information. In this work, we reformulate approximations of the quantum capacity by operator space norms and give both…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…