Related papers: Measuring Energy, Estimating Hamiltonians, and the…
We present exact energy spectrum and eigenfunctions of the one-dimensional hydrogen atom in the presence of the minimal length uncertainty. By requiring the self-adjointness property of the Hamiltonian, we completely determine the…
This paper presents the measurement problem from the point of view of the thermal interpretation of quantum physics introduced in Part II. The measurement of a Hermitian quantity $A$ is regarded as giving an uncertain value approximating…
Early energy-momentum investigations for gravitating systems gave reference frame dependent pseudotensors; later the quasilocal idea was developed. Quasilocal energy-momentum can be determined by the Hamiltonian boundary term, which also…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the…
Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum…
A method is presented in which the ground-state subspace is projected out of a Hamiltonian representation. As a result of this projection, an effective Hamiltonian is constructed where its ground-state coincides with an excited-state of the…
Suppose that a system is known to be in one of two quantum states, $|\psi_1 > $ or $|\psi_2 >$. If these states are not orthogonal, then in conventional quantum mechanics it is impossible with one measurement to determine with certainty…
Locality is a fundamental feature of many physical time evolutions. Assumptions on locality and related structural properties also underlie recently proposed procedures for learning an unknown Hamiltonian from access to the induced time…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
The separation of internal energy into heat and work in quantum thermodynamics is a controversial issue for a long time, and we revisit and solve this problem in this work. It is shown that the Hamiltonian plays dual roles for a quantum…
It is known that temperature estimates of macroscopic systems in equilibrium are most precise when their energy fluctuations are large. However, for nanoscale systems deviations from standard thermodynamics arise due to their interactions…
The energy of gravitating systems has been an issue since Einstein proposed general relativity: considered to be ill defined, having no proper local density. Energy-momentum is now regarded as \emph{quasi-local} (associated with a closed…
The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
A new formulation of the Hamiltonian dynamics of the gravitational field interacting with(non-dissipative) thermo-elastic matter is discussed. It is based on a gauge condition which allows us to encode the six degrees of freedom of the…
In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the…
We critically discuss the measure of very short time intervals. By means of a Gedankenexperiment, we describe an ideal clock based on the occurrence of completely random events. Many previous thought experiments have suggested fundamental…
We construct uncertainty relation for arbitrary finite dimensional PT invariant non-Hermitian quantum systems within a special inner product framework. This construction is led by good observables which are a more general class of…
A quantum-mechanical Hamiltonian with a gravitational potential is derived in the framework of local times. This Hamiltonian is the one used by E. H. Lieb (Bull. Amer. Math. Soc. 22(1990), 1-49) in his explanation of stability and…