Related papers: Strong unitary uncertainty relations
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…
Recently Kosaki proved an inequality for matrices that can be seen as a kind of new uncertainty principle. Independently, the same result was proved by Yanagi, Furuichi and Kuriyama. The new bound is given in terms of Wigner-Yanase-Dyson…
Nonlocality, which is the key feature of quantum theory, has been linked with the uncertainty principle by fine-grained uncertainty relations, by considering combinations of outcomes for different measurements. However, this approach…
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
Entropic uncertainty relations play a fundamental role in quantum information theory. However, determining optimal (tight) entropic uncertainty relations for general observables remains a formidable challenge and has so far been achieved…
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
In this paper, we first provide three general norm inequalities, which are used to give new uncertainty relations of any finite observables and quantum channels via metric-adjusted skew information. The results are applicable to its special…
The standard uncertainty relations (UR) in quantum mechanics are typically used for unbounded operators (like the canonical pair). This implies the need for the control of the domain problems. On the other hand, the use of (possibly…
We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…
We prove a few novel state-dependent uncertainty relations for product as well the sum of variances of two incompatible observables. These uncertainty relations are shown to be tighter than the Roberson-Schr\"odinger uncertainty relation…
Skew information is a pivotal concept in quantum information, quantum measurement, and quantum metrology. Further studies have lead to the uncertainty relations grounded in metric-adjusted skew information. In this work, we present an…
Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the…
Introductory courses on quantum mechanics usually include lectures on uncertainty relations, typically the inequality derived by Robertson and, perhaps, other statements. For the benefit of the lecturers, we present a unified approach --…
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…
In this paper we discuss some aspects of the Heisenberg uncertainty relation, mostly from the point of view of non self-adjoint operators. Some equivalence results, and some refinements of the inequality, are deduced, and some relevant…
The uncertainty principle places a fundamental limit on the accuracy with which we can measure conjugate physical quantities. However, the fluctuations of these variables can be assessed in terms of different estimators. We propose a new…
Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this…