Related papers: L\"{u}ders Theorem for Unsharp Quantum Measurement…
Unsharp spin 1 observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is…
We address the problem of unambiguous discrimination and identification among quantum observables. We set a general framework and investigate in details the case of qubit observables. In particular, we show that perfect discrimination with…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
This paper addresses the question whether a variant of a modal interpretation is conceivable that could accommodate property ascriptions associated with nonorthogonal resolutions of the unity and nonorthogonal families of relative states as…
Measurement is an important scientific activity. In most of science, including classical physics, is may be understood as a way of finding out about the physical world and representing the results numerically. No-go theorems show that…
The question of quantifying the sharpness (or unsharpness) of a quantum mechanical effect is investigated. Apart from sharpness, another property, bias, is found to be relevant for the joint measurability or coexistence of two effects.…
A detailed theory of quantum premeasurement dynamics is presented in which a unitary composite-system operator that contains the relevant object-measuring-instrument interaction brings about the final premeasurement state. It does not…
We consider a second-order parabolic equation in $\bR^{d+1}$ with possibly unbounded lower order coefficients. All coefficients are assumed to be only measurable in the time variable and locally H\"older continuous in the space variables.…
When you measure an observable, A, in Quantum Mechanics, the state of the system changes. This, in turn, affects the quantum-mechanical uncertainty in some non-commuting observable, B. The standard Uncertainty Relation puts a lower bound on…
It has been proposed that measurement in quantum mechanics results from spontaneous breaking of a symmetry of the measuring apparatus and could be a unitary process that preserves coherence. Viewed in this manner, it is argued,…
In this paper, we present a collection of results on the observability of quantum mechanical systems, in the case the output is the result of a discrete nonselective measurement. By defining an effective observable we extend previous…
In the study of Heisenberg's error-disturbance relation, it is commonly believed that the non-unitary change of states hinders us from deducing the information encoded in original states about subsequently measured observable. However, we…
Quantum coherence can be used to infer the presence of a detector without triggering it. Here we point out that, according to quantum mechanics, such interaction-free measurements cannot be perfect, i.e., in a single-shot experiment one has…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
In this second paper, we develop the full mathematical structure of the algebra of the pseudo-observables, in order to solve the quantum measurement problem. Quantum state vectors are recovered but as auxiliary pseudo-observables storing…
We study generating joint measurements by operating on the input quantum state with a broadcasting channel followed by local measurements on the two outputs of the broadcasting channel. Although, due to perfect broadcasting or cloning being…
Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable…