Related papers: Non-commuting Observables are Jointly Measureable …
The well-known two-slit interference is understood as a special relation between observable (localization at the slits) and state (being on both slits). Relation between an observable and a quantum state is investigated in the general case.…
I consider the tradeoff between the information gained about an initially unknown quantum state, and the disturbance caused to that state by the measurement process. I show that for any distribution of initial states, the…
Measurements map the value of a target observable onto a meter shift, resulting in a meter readout that combines the initial statistics of the meter state with the quantum statistics of the target observable. Even in the limit of weak…
We consider a special form of state discrimination in which after the measurement we are given additional information that may help us identify the state. This task plays a central role in the analysis of quantum cryptographic protocols in…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
The core of Heisenberg's heuristic argument for the uncertainty principle, involving the famous $\gamma$-ray microscope $\textit{Gedankenexperiment}$, hinges upon the existence of measurements that irreversibly alter the state of the system…
The Heisenberg-Robertson uncertainty relation quantitatively expresses the impossibility of jointly sharp preparation of incompatible observables. However it does not capture the concept of incompatible observables because it can be trivial…
We consider a range of "theories" that violate the uncertainty relation for anti-commuting observables derived in [JMP, 49, 062105 (2008)]. We first show that Tsirelson's bound for the CHSH inequality can be derived from this uncertainty…
Measurement error in the observed values of the variables can greatly change the output of various causal discovery methods. This problem has received much attention in multiple fields, but it is not clear to what extent the causal model…
We show that any sequence of measurements on a permutationally-symmetric (pure or mixed) multi-qubit string leaves the unmeasured qubit substring also permutationally-symmetric. In addition, we show that the measurement probabilities for an…
This study confirms a local trade-off between information and disturbance in quantum measurements. It is represented by the correlation between the changes in these two quantities when the measurement is slightly modified. The correlation…
Using formal definitions for measurement precision {\epsilon} and disturbance (measurement backaction) {\eta}, Ozawa [Phys. Rev. A 67, 042105 (2003)] has shown that Heisenberg's claimed relation between these quantities is false in general.…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
Employing an effective formalism for decaying system we are able to investigate Heisenberg's uncertainty relation for observables measured at accelerator facilities. In particular we investigate the neutral K--meson system and show that,…
We report a refinement of Robertson-Schroedinger uncertainty relation via Wigner-Yanase skew information. Besides the well known quantum uncertainty arising from the noncommutativity of observables, there is classical uncertainty arising…
We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality…
Quantum theory famously entails the existence of incompatible measurements; pairs of observables which cannot be simultaneously measured to arbitrary precision. Incompatibility is widely regarded to be a uniquely quantum phenomenon, linked…
Inferring the causal effect of a non-randomly assigned exposure on an outcome requires adjusting for common causes of the exposure and outcome to avoid biased conclusions. Notwithstanding the efforts investigators routinely make to measure…
The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…