Related papers: Quantifying incompatibility beyond entropic uncert…
Quantum instruments describe outcome probability as well as state change induced by measurement of a quantum system. Incompatibility of two instruments, i. e. the impossibility to realize them simultaneously on a given quantum system,…
Quantum multiparameter metrology is hindered by incompatibility issues, such as finding a single probe state (probe incompatibility) and a single measurement (measurement incompatibility) optimal for all parameters. The simultaneous…
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…
We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task with partial intermediate information. This is done by showing that only incompatible measurements allow for an efficient use of…
We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and…
We discuss the entropic criterion for separability of compound quantum systems for general non-additive entropic forms based on arbitrary concave functions $f$. For any separable state, the generalized entropy of the whole system is shown…
A quantum observable and a channel are considered compatible if they form parts of the same measurement device, otherwise they are incompatible. Constrains on compatibility between observables and channels can be quantified via relations…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
Measurements in quantum theory can fail to be jointly measurable. Like entanglement, this incompatibility of measurements is necessary but not sufficient for violating Bell inequalities. The (in)compatibility relations among a set of…
One of the most remarkable features of quantum physics is that attributes of quantum objects, such as the wave-like and particle-like behaviors of single photons, can be complementary in the sense that they are equally real but cannot be…
The notion coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review…
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…
The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand…
Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies, such as quantum computation, quantum communication and quantum metrology. Yet, their quantification, rather than…
The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…
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 give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
A trade-off relation on our knowledge about two noncommuting observables of a qubit system in simultaneous measurement is formulated. The obtained inequality offers a quantitative information-theoretic representation of Bohr's principle of…
Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an…
We consider the problem of certifying measurement incompatibility in a prepare-and-measure (PM) scenario. We present different families of sets of qubit measurements which are incompatible, but cannot lead to any quantum over classical…