Related papers: On the connection between Complementarity and Unce…
Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays the important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
In terms of operator, the two complementary quantities, the predictability and visibility, are reinvestigated in a two-way interferometer. One Hermitian operator and one non-Hermitian operator (composed of two Hermitian operators) are…
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…
A model of the Einstein-Bohr double-slit experiment is formulated in a fully quantum theoretical setting. In this model, the state and dynamics of a movable wall that has the double slits in it, as well as the state of a particle incoming…
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations…
Uncertainty principle, a fundamental principle in quantum physics, has been studied intensively via various uncertainty inequalities. Here we derive an uncertainty equality in terms of linear entropy, and show that the sum of uncertainty in…
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by $N$ linear combinations of position and momentum observables. The state-independent bounds depend on their…
In [Berta 2014 Entanglement], uncertainty relations in the presence of quantum memory was formulated for mutually unbiased bases using conditional collision entropy. In this paper, we generalize their results to the mutually unbiased…
Which-path information of a quantum particle in interferometers is the key to infer the past of quantum particle. It arises many extensive discussions including quantum complementarity and path-visibility relation. The basic of these…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
Complementarity, the incomplete nature of a quantum measurement - a core concept in quantum mechanics - stems from the choice of the measurement apparatus. The notion of complementarity is closely related to Heisenberg's uncertainty…
We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the B\"ottcher-Wenzel inequality. The first relation is mathematically proven, while the second, tighter relation is…
The Mach-Zehnder interferometric setup quantitatively characterizing the wave-particle duality implements in fact a joint measurement of two unsharp observables. We present a necessary and sufficient condition for such a pair of unsharp…
Consideration of the von Neumann measurement process underlying interference experiments shows that the uncertainty in the incoming wave, responsible for its interference, translates during measurement into an uncertainty at the measuring…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator…
The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We…
A pair of uncertainty relations relevant for quantum states of multislit interferometry is derived, based on the mutually commuting "modular" position and momentum operators and their complementary counterparts, originally introduced by…
Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such…