Related papers: Stronger sum uncertainty relations for non-Hermiti…
We formulate an inseparability criterion based on the recently derived generalized Schr\"odinger-Robertson uncertainty relation (SRUR) [Ivan {\it et al.} J. Phys. A :Math. Theor. {\bf 45}, 195305 (2012)] together with the negativity of…
A non-hermitian deformation of the one-dimensional transverse Ising model is shown to have the property of quasi-hermiticity. The transverse Ising chain is obtained from the starting non-hermitian Hamiltonian through a similarity…
We analyze general uncertainty relations and we show that there can exist such pairs of non--commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…
We revisit the Extended Uncertainty Principle (EUP) from an operational viewpoint, replacing wavefunction-based widths with apparatus-defined position constraints such as a finite slit of width $\Delta x$ or a geodesic ball of radius $R$.…
In recent decades, an important shift has taken place with the growing role of non-Hermitian quantum mechanics. What makes this framework remarkable is that the eigenvalues of the Hamiltonians involved can still be real, just as in the…
Thermodynamic uncertainty relations (TURs) place strict bounds on the fluctuations of thermodynamic quantities in terms of the associated entropy production. In this work we identify the tightest (and saturable) matrix-valued TUR that can…
Evolutions under non-Hermitian Hamiltonians with unbroken $\mathcal{PT}$ symmetry can be considered unitary under appropriate choices of inner products, facilitated by the so-called metric operator. While it is understood that the choice of…
The canonical Robertson-Schr\"{o}dinger uncertainty relation provides a loose bound for the product of variances of two non-commuting observables. Recently, several tight forward and reverse uncertainty relations have been proved which go…
It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of…
In the framework of quasi-Hermitian quantum mechanics the eligible operators of observables may be non-Hermitian, $A_j\neq A_j^\dagger$, $j=1,2, \ldots,K$. In principle, the standard probabilistic interpretation of the theory can be…
Uncertainty relations are shown to have nothing specific for quantum mechanics, being the general property valid for arbitrary function. A wave function of a particle having precisely defined position and momentum in QM simultaneously is…
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a…
Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the…
The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand…
We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum…
We provide an extended acount of the recent statistical mechanical theory of gauge invariance against operator shifting in quantum many-body systems (arXiv:2509.20494). The gauge transformation is enacted by a shifting superoperator that…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
An open U_q(sl_2)-invariant spin chain of spin S and length N with inhomogeneous coupling is investigated as an example of a non-Hermitian (quasi-Hermitian) model. For several particular cases of such a chain, the ranges of the deformation…
A series of recent papers ``Faster than Hermitian Quantum Mechanics'' and related articles made a point of the possibility of a non-Hermitian, but PT-symmetric, operator to play the role of a Hamiltonian. In particular, they show that with…
Heisenberg's measurement uncertainty relations (MUR) of two quantum observables are essential for contemporary researches in quantum foundations and quantum information science. Going beyond, here we report the first experimental test of…