Related papers: The compatibility dimension of quantum measurement…
We propose a test for certifying the dimension of a quantum system: store in it a random $n$-bit string, in either the computational or the Hadamard basis, and later check that the string can be mostly recovered. The protocol tolerates…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
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 propose a new measure of relative incompatibility for a quantum system with respect to two non-commuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is…
We present a derivation and experimental implementation of a dimension-dependent contextuality inequality to certify both the quantumness and dimensionality of a given system. Existing methods for certification of the dimension of quantum…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be…
We characterize minimal measurement setups for validating the quantum coherence of an unknown quantum state. We show that for a $d$-level system, the optimal strategy consists of measuring $d$ orthonormal bases such that each measured basis…
The maximum observable correlation between the two components of a bipartite quantum system is a property of the joint density operator, and is achieved by making particular measurements on the respective components. For pure states it…
The concept of compatibility originally emerged as a synonym for the commutativity of observables and later evolved into the notion of measurement compatibility. In any case, however, it has remained predominantly algebraic in nature, tied…
We have determined numerically the maximum quantum violation of over 100 tight bipartite Bell inequalities with two-outcome measurements by each party on systems of up to four dimensional Hilbert spaces. We have found several cases,…
Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum…
We investigate the universal asymmetric cloning of states in a Hilbert space of arbitrary dimension. We derive the class of optimal and fully asymmetric 1->3 cloners, which produce three copies, each having a different fidelity. A simple…
Complementarity is one of the main features of quantum physics that radically departs from classical notions. Here we consider the limitations that this principle imposes due to the unpredictability of measurement outcomes of incompatible…
We propose a modified metric based on the Hilbert-Schmidt norm and adopt it to define a rescaled version of the geometric measure of quantum discord. Such a measure is found not to suffer from the pathological dependence on state purity.…
We investigate the most general mechanisms that lead to perfect synchronization of the quantum states of all subsystems of an open quantum system starting from an arbitrary initial state. We provide a necessary and sufficient condition for…
The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on…
We investigate the optimal approximation to triple incompatible quantum measurements within the framework of statistical distance and joint measurability. According to the lower bound of the uncertainty inequality presented in [Physical…
Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here…
The Cram\'er-Rao bound captures completely the performance of single-parameter quantum sensors. On the other hand, its extension to multiple parameters demands more caution. Different aspects need to be captured at once, including,…