Related papers: Complementarity-based complementarity: the choice …
Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$…
We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states…
We derive a new memory-assisted entropic uncertainty relation for non-degenerate Hermitian observables where both quantum correlations, in the form of conditional von Neumann entropy, and quantum discord between system and memory play an…
Uncertainty relation usually is one of the most important features in quantum mechanics, and is the backbone of quantum theory, which distinguishes from the rule in classical counterpart. Specifically, entropy-based uncertainty relations…
We formulate a general complementarity relation starting from any Hermitian operator with discrete non-degenerate eigenvalues. We then elucidate the relationship between quantum complementarity and the Heisenberg-Robertson's uncertainty…
Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability…
Unextendible sets of Mutually Unbiased Bases (MUBs) are examined from the point of view of complementary subalgebras. We show, that the linear span of less than $d+1$ factors of $M_d \otimes M_d$ does not contain pure states, and therefore…
Quantum measurements necessarily disturb the state of physical system. Once we perform a complete measurement, the system undergoes decoherence and loses its coherence. If there is no disturbance, the state retains all of its coherence. It…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets.…
Uncertainty principle is an inherent nature of quantum system that undermines the precise measurement of incompatible observables and hence the applications of quantum theory. Entanglement, another unique feature of quantum physics, was…
The well-known Robertson-Schr\"odinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…
With the aid of a quantum memory, the uncertainty about the measurement outcomes of two incompatible observables of a quantum system can be reduced. We investigate this measurement uncertainty bound by considering an additional quantum…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
We investigate the product form uncertainty relations of variances for $n\,(n\geq 3)$ quantum observables. In particular, tight uncertainty relations satisfied by three observables has been derived, which is shown to be better than the ones…
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…
Quantum uncertainty is described here in two guises: indeterminacy with its concomitant indeterminism of measurement outcomes, and fuzziness, or unsharpness. Both features were long seen as obstructions of experimental possibilities that…
Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum…