Related papers: Measuring Energy, Estimating Hamiltonians, and the…
All energy measurements of a quantum system are prone to inaccuracies. In particular, if such measurements are carried over a finite period of time the accuracy of the result is affected by the length of that period. Here I show an upper…
The time-energy uncertainty relation is often invoked as a heuristic explanation for virtual particles in interacting quantum field theories. However, this interpretation breaks down upon closer scrutiny for several reasons. Although…
We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation." Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time…
It is difficult to discriminate between the state of initial time $t_0$ and that of time $t_0+\Delta t$. The task of discriminating between the two states can be interpreted as the hypothesis testing problem as to a state $\rho$ deciding…
We prove the uncertainty relation $\sigma_T \, \sigma_E \geq \hbar/2$ between the time $T$ of detection of a quantum particle on the surface $\partial \Omega$ of a region $\Omega\subset \mathbb{R}^3$ containing the particle's initial wave…
A projective measurement of energy (PME) on a quantum system is a quantum measurement, determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by…
Uncertainty relations play a crucial role in quantum mechanics. Well-defined methods exist for the derivation of such uncertainties for pairs of observables. Other approaches also allow the formulation of time-energy uncertainty relations,…
Preparing low energy states is a central challenge in quantum computing and quantum complexity theory. Several known approaches to prepare low energy states often get stuck in suboptimal states, such as high energy eigenstates (or low…
We derive the expression for the energy uncertainty of the final state of a decay of an unstable quantum state prepared at the initial time $t=0$. This expression is function of the time $t$ at which a measurement is performed to determine…
The resource-theoretic approach to quantum thermodynamics assumes complete knowledge of the thermal equilibrium against which thermodynamic resources are defined. In practice, however, this state is determined by the system Hamiltonian and…
The nonequilibrium thermodynamics of an open (classical or quantum) system in strong contact with a single heat bath can be conveniently described in terms of the Hamiltonian of mean force. However, the conventional formulation is limited…
A quantum clock working as a control device is examined. The quality of the control process is characterized by the magnitude of deviation of perturbed state from unperturbed state of the controlled system. Uncertainty relations that relate…
This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case…
Over the last few decades, developments in the physical limits of computing and quantum computing have increasingly taught us that it can be helpful to think about physics itself in computational terms. For example, work over the last…
Quantum measurements are our eyes to the quantum systems consisting of a multitude of microscopic degrees of freedom. However, the intrinsic uncertainty of quantum measurements and the exponentially large Hilbert space pose natural barriers…
I review some recent results showing that the physics of negative energy densities, as predicted by relativistic quantum field theories, is more complicated than has generally been appreciated. On the one hand, in external potentials where…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
Recently, we have suggested some semi-quantitative Hamiltonian for an electron in a hydrogen atom in a weak gravitational field, which takes into account quantum effects of electron motion in the atom. We have shown that this Hamiltonian…
Using a recent construction of observables characterizing the time of occurence of an effect in quantum theory, we present a rigorous derivation of the standard time-energy uncertainty relation. In addition, we prove an uncertainty relation…
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form $(\Delta P)(\Delta Q)\geq C\hbar$, where the `uncertainties' quantify the difference between the marginals of the…