Related papers: Retrodiction beyond the Heisenberg uncertainty rel…
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…
Quantum mechanics describes seemingly paradoxical relations between the outcomes of measurements that cannot be performed jointly. In Hilbert space, the outcomes of such incompatible measurements are represented by non-orthogonal states. In…
The density matrix yields probabilistic information about the outcome of measurements on a quantum system, but it does not distinguish between classical randomness in the preparation of the system and entanglement with its environment.…
Heisenberg's uncertainty relations for measurement quantify how well we can jointly measure two complementary observables and have attracted much experimental and theoretical attention recently. Here we provide an exact tradeoff between the…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
In quantum metrology, entanglement represents a valuable resource that can be used to overcome the Standard Quantum Limit (SQL) that bounds the precision of sensors that operate with independent particles. Measurements beyond the SQL are…
The existence of a minimal measurable length is a common feature of various approaches to quantum gravity such as string theory, loop quantum gravity and black-hole physics. In this scenario, all commutation relations are modified and the…
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 significance of this "exact"…
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form $(\Delta P)(\Delta Q)\geq C\hbar$, where the `uncertainties' quantify the difference between the marginals of the…
We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation…
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…
We ask which is the best strategy to reveal uncertainty relations between comple- mentary observables of a continuous variable system for coarse-grained measurements. This leads to the derivation of new uncertainty relations for…
This paper presents the uncertainty related to position and momentum localization of a quantum state in terms of entropic uncertainty relations. We slightly improve the inequality given in [Phys. Rev. A 74, 052101 (2006)] and introduce a…
It is well known that the problem of divergence in the physical interpretation of quantum mechanics originating from the uncertainty principle has not yet been resolved. Attempting to clear the constraints and confusion of this situation…
The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by…
From the very beginning, Quantum Mechanics has been accompanied by crucial foundational questions: the possibility of visualizing physical processes, the limits of measurement epitomized by the Heisenberg uncertainty principle, the…
Quantum metrology promises improved sensitivity in parameter estimation over classical procedures. However, there is an extensive debate over the question how the sensitivity scales with the resources (such as the average photon number) and…
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
The Heisenberg's error-disturbance relation is a cornerstone of quantum physics. It was recently shown to be not universally valid and two different approaches to reformulate it were proposed.The first one focuses on how error and…
In Heisenberg's error-disturbance relation for electron position measurement, the measurement error must be the one that determines the uncertainty in the electron position just after the measurement. It is the resolution $\epsilon(x_t)$…