Related papers: Subfactors and quantum information theory
Von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are however static processes that do not adapt to the states they measure. Advances in the field of adaptive…
It is proposed to define "quantumness" of a system (micro or macroscopic, physical, biological, social, political) by starting with understanding that quantum mechanics is a statistical theory. It says us only about probability…
We introduce information-theoretic definitions for noise and disturbance in quantum measurements and prove a state-independent noise-disturbance tradeoff relation that these quantities have to satisfy in any conceivable setup. Contrary to…
We develop a theory of quantum sufficiency on real *-subalgebras and real Jordan algebras. In contrast to the conventional formulation, which is based on families of states, complex completely positive coarse-grainings, and Radon-Nikodym…
This review presents an entry-level introduction to topological quantum computation -- quantum computing with anyons. We introduce anyons at the system-independent level of anyon models and discuss the key concepts of protected fusion…
Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as…
Decompositional theories describe the ways in which a global physical system can be split into subsystems, facilitating the study of how different possible partitions of a same system interplay, e.g. in terms of inclusions or signalling. In…
Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the…
This paper addresses the problem of how much information we can extract without disturbing a statistical experiment, which is a family of partially known normal states on a von Neumann algebra. We define the classical part of a statistical…
Characterization of quantum objects, being them states, processes, or measurements, complemented by previous knowledge about them is a valuable approach, especially as it leads to routine procedures for real-life components. To this end,…
Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
A fully quantum version of the Witten-Olive analysis of the central charge in the N=1 Wess-Zumino model in $d=2$ with a kink solution is presented by using path integrals in superspace. We regulate the Jacobians with heat kernels in…
The operator algebra of fermionic modes is isomorphic to that of qubits, the difference between them is twofold: the embedding of subalgebras corresponding to mode subsets and multiqubit subsystems on the one hand, and the parity…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
We establish a generalisation of the fundamental state convertibility theorem in quantum information to the context of bipartite quantum systems modelled by commuting semi-finite von Neumann algebras. Namely, we establish a generalisation…
The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent i.i.d. copies of the state are available,…
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum…
Quantum coherence is a fundamental feature of quantum mechanics and an underlying requirement for most quantum information tasks. In the resource theory of coherence, incoherent states are diagonal with respect to a fixed orthonormal basis,…
Quantum coherence constitutes a foundational characteristic of quantum mechanics and is integral to emerging quantum resource theories. However, quantum coherence is severely restricted by environmental noise in general quantum processing,…