Related papers: Complementarity and uncertainty in a two-way inter…
The principle of complementarity is quantified in two ways: by a universal uncertainty relation valid for arbitrary joint estimates of any two observables from a given measurement setup, and by a general uncertainty relation valid for…
Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily…
By means of the technique of integration within an ordered product of operators and Dirac notation, we introduce a new kind of asymmetric integration projection operators in entangled state representations. These asymmetric projection…
We develop a duality theory for unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency…
Uncertainty relations are often considered to be a measure of incompatibility of noncommuting observables. However, such a consideration is not valid in general, motivating the need for an alternate measure that applies to any set of…
Relations connecting violation of any Bell inequalities and the complementarity between visibility and distinguishability in the interferometric experiments with different sources of decoherence are presented. A boundary of local-realistic…
Standard quantum physics prevents the existence of a joint statistics for complementary observables. Nevertheless, a joint distribution for complementary observables can be derived from their imperfect simultaneous measurement followed by a…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…
Two complementary observables can be measured simultaneously so that the exact individual distributions can be recovered by a proper data inversion. We apply this program to the paradigmatic example of the Young interferometer from the…
We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability $D$ quantifying the amount of which-way (WW) information to the fringe visibility $V$ characterizing the wave feature of a quantum…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
We find that a broken PT-symmetry operator when interacts with suitable Hermitian operator, new system becomes completely un-broken PT symmetry. Further on varying the contribution of Hermiticity one can delay or control the broken…
We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems, with number treated as a discrete Hermitian…
We provide an analysis of complementarity via a suitably designed classicalmodel that leads to a set of inequalities that can be tested by means ofunsharp measurements. We show that, if the measured statistics does notfulfill the…
We introduce a generalization of symmetric measurements to collections of unequinumerous positive, operator-valued measures (POVMs). For informationally complete sets, we propose construction methods from orthonormal Hermitian operator…
We study both the wave-like behavior and particle-like behavior in a general Mach-Zehnder interferometer with its asymmetric beam splitter. A error-free measurement in the detector is used to extract the which-path information. The fringe…
It is well known that the Mach-Zender interferometer exhibits a trade-off between the a priori which-path knowledge and the visibility of its interference pattern. This trade-off is expressed by the inequality $\mathcal{P}^2 + \mathcal{V}^2…
Output controllability and functional observability are properties that enable, respectively, the control and estimation of part of the state vector. These notions are of utmost importance in applications to high-dimensional systems, such…
We propose a new measure of relative incompatibility for a quantum system with respect to two non-commuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is…
How much unavoidable randomness is generated by a Positive Operator Valued Measure (POVM)? We address this question using two complementary approaches. First we study the variance of a real variable associated to the POVM outcomes. In this…