Related papers: Universally valid uncertainty relations in general…
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…
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…
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…
We outline a new model in which generalised uncertainty relations are obtained without modified commutation relations. While existing models introduce modified phase space volumes for the canonical degrees of freedom, we introduce new…
The uncertainty principle being a cornerstone of quantum mechanics, it is surprising that in nearly 90 years there have been no direct tests of measurement uncertainty relations. This lacuna was due to the absence of two essential…
We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is…
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify…
The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of…
The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in…
Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {\it uncertainty relation} is a generic term for various trade-off relations in nature. In…
We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. There are studied uncertainty relations for sums of…
The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within 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…
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 short note we show how the Generalised Uncertainty Principle (GUP) and the Extended Uncertainty Principle (EUP), two of the most common generalised uncertainty relations proposed in the quantum gravity literature, can be derived…
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…
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 present the entropic uncertainty relations for multiple measurement settings in quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory. They take concise forms which can…
Finite tight frames are interesting in various topics including questions of quantum information. Each complex tight frame leads to a resolution of the identity in the Hilbert space. Symmetric informationally complete measurements are a…
We use quantum estimation theory to derive a thermodynamic uncertainty relation in Markovian open quantum systems, which bounds the fluctuation of continuous measurements. The derived quantum thermodynamic uncertainty relation holds for…