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The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved…
Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed…
Quantum reservoir computing (QRC) harnesses driven quantum dynamics for time-series processing, yet the mechanisms behind the differing performance levels across its many implementations remain unclear. We show that apparently unrelated…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
Resource theories are broad frameworks that capture how useful objects are in performing specific tasks. In this paper we devise a formal resource theory quantum measurements, focusing on the ability of a measurement to acquire information.…
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty…
Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
We review the basic idea behind resource theories, where we quantify quantum resources by specifying a restricted class of operations. This divides the state space into various sets, including states which are free (because they can be…
Preserving entanglement is a crucial dynamical process for entanglement-based quantum computation and quantum-information processes, such as one-way quantum computing and quantum key distribution. However, the problem of quantifying the…
Randomness is a key feature of quantum physics. Heisenberg's uncertainty principle reveals the existence of an intrinsic noise, usually explored through Gaussian squeezed states. Due to their insufficiency for quantum advantage, the focus…
The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary…
Finding physical principles lying behind quantum mechanics is essential to understand various quantum features, e.g., the quantum correlations, in a theory-independent manner. Here we propose such a principle, namely, no disturbance without…
When quantifying the mixing properties of a quantum dynamical system in terms of dynamical entropy, the following scheme appears natural: observe the state of the system at regular time intervals while it evolves and determine the entropy…
Quantum coherence quantifies the amount of superposition in a quantum system, and is the reason and resource behind several phenomena and technologies. It depends on the natural basis in which the quantum state of the system is expressed,…
The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the…
Control at the interface between the classical and the quantum world is fundamental in quantum physics. In particular, how classical control is enhanced by coherence effects is an important question both from a theoretical as well as from a…
The notion of nonlocality implicitly implies there might be some kind of spooky action at a distance in nature, however, the validity of quantum mechanics has been well tested up to now. In this work it is argued that the notion of…
The inherent connection between noise and disturbance is one of the most fundamental features of quantum measurements. In the two well-known extreme cases a measurement either makes no disturbance but then has to be totally noisy or is as…
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides…