Related papers: Optimal estimates and joint measurement uncertaint…
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…
We consider joint measurement of two and three unsharp qubit observables through an Arthur-Kelly type joint measurement model for qubits. We investigate the effect of initial state of the detectors on the unsharpness of the measurement as…
Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum…
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A…
According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
Information-theoretic definitions for the noise associated with a quantum measurement and the corresponding disturbance to the state of the system have recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401 (2014)]. These…
Knowledge of optimal quantum measurements is important for a wide range of situations, including quantum communication and quantum metrology. Quantum measurements are usually optimised with an ideal experimental realisation in mind. Real…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…
Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not…
In Quantum Physics it is not always possible to directly perform the measurement of an obsevable; in some of these cases, however, its value can be {\sl detected}, i.e. it can be inferred by measuring {\sl another} observable characterized…
We consider the problem of estimating the ensemble average of an observable on an ensemble of equally prepared identical quantum systems. We show that, among all kinds of measurements performed jointly on the copies, the optimal unbiased…
We combine traditional pointer-based simultaneous measurements of conjugate observables with the concept of quantum Brownian motion of multipartite systems to phenomenologically model simultaneous measurements of conjugate observables in a…
The measurement outcomes of two incompatible observables on a particle can be precisely predicted when it is maximally entangled with a quantum memory, as quantified recently [Nature Phys. 6, 659 (2010)]. We explore the behavior of the…
We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive.…
We derive new inequalities for the probabilities of projective measurements in mutually unbiased bases of a qudit system. These inequalities lead to wider ranges of validity and tighter bounds on entropic uncertainty inequalities previously…
Incompatibility of quantum measurements is of fundamental importance in quantum mechanics. It is closely related to many nonclassical phenomena such as Bell nonlocality, quantum uncertainty relations, and quantum steering. We study the…
A complete theory of overmeasurement by measuring refinements of observables is presented. It encompasses a wider set of functions of observ- ables (coarsenings) . Thus the theory has a broad potential application.It is applied to a…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The statistics of complementary…