Related papers: Mutual Unbiasedness in Coarse-grained Continuous V…
Mutual unbiasedness of the eigenstates of phase-space operators-such as position and momentum, or their standard coarse grained versions-exists only in the limiting case of infinite squeezing. In [Phys. Rev. Lett. 120, 040403 (2018)] it was…
Most of the fundamental characteristics of quantum mechanics, such as non-locality and contextuality, are manifest in discrete, finite-dimensional systems. However, many quantum information tasks that exploit these properties cannot be…
Coarse graining is a common imperfection of realistic quantum measurement, obstructing the direct observation of quantum features. Under highly coarse-grained measurement, we experimentally detect the continuous-variable nonclassicality of…
Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum…
We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices.…
One of the most important and useful entropic uncertainty relations concerns a $d$ dimensional system and two mutually unbiased measurements. In such a setting, the sum of two information entropies is lower bounded by $\ln d$. It has…
Continuous variables systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as…
The task of measuring in two mutually unbiased bases is central to many quantum information protocols, as well as being of fundamental interest. Increasingly, there is an experimental focus on generating and controlling high-dimensional…
We develop a systematic coarse graining procedure for systems of $N$ qubits. We exploit the underlying geometrical structures of the associated discrete phase space to produce a coarse-grained version with reduced effective size. Our…
We derive a fine-grained uncertainty relation for the measurement of two incompatible observables on a single quantum system of continuous variables, and show that continuous variable systems are more uncertain than discrete variable…
Mutually unbiased measurements (MUMs) are generalized from the concept of mutually unbiased bases (MUBs) and include the complete set of MUBs as a special case, but they are superior to MUBs as they do not need to be rank one projectors. We…
We present a joint-measurement uncertainty relation for a pair of mean square deviations of canonical variables averaged over Gaussian distributed quantum optical states. Our Bayesian formulation is free from the unbiasedness assumption,…
We study the entanglement detection by using mutually unbiased measurements and provide a quantum separability criterion that can be experimentally implemented for arbitrary $d$-dimensional bipartite systems. We show that this criterion is…
The connection between coarse-graining of measurement and emergence of classicality has been investigated for some time, if not well understood. Recently in (PRL $\textbf{112}$, 010402, (2014)) it was pointed out that coarse-graining…
The coarse-graining approach to deriving the quantum Markovian master equation is revisited, with close attention given to the underlying approximations. It is further argued that the time interval over which the coarse-graining is…
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…
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…
We investigate correlations among complementary observables. In particular, we show how to take advantage of mutually unbiased bases (MUBs) for the efficient detection of entanglement in arbitrarily high-dimensional, multipartite and…
We first present a generalization of the Robertson-Heisenberg uncertainty principle. This generalization applies to mixed states and contains a covariance term. For faithful states, we characterize when the uncertainty inequality is an…
A new procedure for coarse-graining dynamical triangulations is presented. The procedure provides a meaning for the relevant value of observables when "probing at large scales", e.g. the average scalar curvature. The scheme may also be…