Related papers: Stronger sum uncertainty relations for non-Hermiti…
In quantum theory, a physical observable is represented by a Hermitian operator as it admits real eigenvalues. This stems from the fact that any measuring apparatus that is supposed to measure a physical observable will always yield a real…
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…
Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity…
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully…
Recently, Maccone and Pati [Phys. Rev. Lett. {\bf 113}, 260401 (2014)] derived few inequalities among variances of incompatible operators which they called stronger uncertainty relations, stronger than Heisenberg-Robertson or Schrodinger…
Based on mixedness definition as M=1-tr(\r{ho}^2), we obtain a new variance-based uncertainty equality along with an inequality for Hermitian operators of a single-qubit system. The obtained uncertainty equality can be used as a measure of…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
We prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable…
The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
We construct a multi-observable uncertainty equality as well as an inequality based on the sum of standard deviations in the qubit system. The obtained equality indicates that the uncertainty relation can be expressed more accurately, and…
The existence of incompatible observables constitutes one of the most prominent characteristics of quantum mechanics (QM) and can be revealed and formalized through uncertainty relations. The Heisenberg-Robertson-Schr\"odinger uncertainty…
Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…
Excited bound states are often understood within scattering based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert…
The effects of any quantum measurement can be described by a collection of measurement operators {M_m} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the…
We present a mathematical formalism of non-Hermitian quantum mechanics, following the Dirac-von Neumann formalism of quantum mechanics. In this formalism, the state postulate is the same as in the Dirac-von Neumann formalism, but the…
Constructive techniques to establish state-independent uncertainty relations for the sum of variances of arbitrary two observables are presented. We investigate the range of simultaneously attainable pairs of variances, which can be applied…
We examine the so-called thermodynamic uncertainty relation (TUR), a cost-precision trade-off relationship in transport systems. Based on the fluctuation symmetry, we derive a condition on the validity of the TUR for general nonequilibrium…