Related papers: Geometric lower bound for a quantum coherence meas…
We plot the geometry of several distance-based quantifiers of coherence for Bell-diagonal states. We find that along with both $l_{1}$ norm and relative entropy of coherence changes continuously from zero to one, their surfaces move from…
Quantum information processing faces a significant hurdle: noise. Different noise sources induce varying errors in quantum operations depending on the underlying dynamics. To gain a deeper understanding of these error mechanisms, we…
A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general…
Geometric quantum discord is a well-defined measure of quantum correlation if Schatten 1-norm (trace norm) is adopted as a distance measure. Here, we analytically investigate the dynamical behavior of the 1-norm geometric quantum discord…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
We study the fuzzy spaces (as special examples of noncommutative manifolds) with their quasicoherent states in order to find their pertinent metrics. We show that they are naturally endowed with two natural "quantum metrics" which are…
The Loomis-Whitney inequality, and the more general Uniform Cover inequality, bound the volume of a body in terms of a product of the volumes of lower-dimensional projections of the body. In this paper, we prove stability versions of these…
We derive an asymptotic lower bound on the Bayes risk when N identical quantum systems whose state depends on a vector of unknown parameters are jointly measured in an arbitrary way and the parameters of interest estimated on the basis of…
Landauer's principle introduces a symmetry between computational and physical processes: erasure of information, a logically irreversible operation, must be underlain by an irreversible transformation dissipating energy. Monitoring micro-…
We discuss some properties of the quantum discord based on the geometric distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {\bf 105}, 190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how good the…
We derive upper bounds for Hilbert-Schmidt's quantum coherence of general states of a $d$-level quantum system, a qudit, in terms of its incoherent uncertainty, with the latter quantified using the linear and von Neumann's entropies of the…
We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able…
A symmetric measure of quantum correlation based on the Hilbert-Schmidt distance is presented in this paper. For two-qubit states, we simplify considerably the optimization procedure so that numerical evaluation can be performed…
The metric-adjusted skew information establishes a connection between the geometrical formulation of quantum statistics and the measures of quantum information. We study uncertainty relations in product and summation forms of…
Quantum metrology is a promising practical use case for quantum technologies, where physical quantities can be measured with unprecedented precision. In lieu of quantum error correction procedures, near term quantum devices are expected to…
Quantum error correcting (QEC) codes protect quantum information against environmental noise. Computational errors caused by the environment change the quantum state within the qubit subspace, whereas quantum erasures correspond to the loss…
Most quantum metrology protocols harness highly entangled probe states and globally accessible measurements to surpass the standard quantum limit. However, it is challenging to satisfy these requirements in realistic many-body sensors. We…
In this work, we derive state-dependent uncertainty relations (uncertainty equalities) in which commutators of incompatible operators (not necessarily Hermitian) are explicitly present and state-independent uncertainty relations based on…