Related papers: Is the SIC Outcome There When Nobody Looks?
Generalized symmetric informationally complete (SIC) measurements are SIC measurements that are not necessarily rank one. They are interesting originally because of their connection with rank-one SICs. Here we reveal several merits of…
Minimal Informationally Complete quantum measurements, or MICs, illuminate the structure of quantum theory and how it departs from the classical. Central to this capacity is their role as tomographically complete measurements with the…
The physical problem behind informationally complete (IC) measurements is determining an unknown state statistically by measurement outcomes, known as state tomography. It is of central importance in quantum information processing such as…
Symmetric informationally complete measurements (SICs) are elegant, celebrated and broadly useful discrete structures in Hilbert space. We introduce a more sophisticated discrete structure compounded by several SICs. A SIC-compound is…
Standard quantum measurements are projective. However, the full scope of quantum measurements is represented by positive operator-valued measures (POVMs) and many of these break the limitations of projective measurements as resources in…
In this paper we examine a generalization of the symmetric informationally complete POVMs. SIC-POVMs are the optimal measurements for full quantum tomography, but if some parameters of the density matrix are known, then the optimal SIC POVM…
Coherence, treated as a resource in quantum information theory, is a basis-dependent quantity. Looking for states that have constant coherence under canonical changes of basis yields highly symmetric structures in state space. For the case…
The unpredictability of quantum physics gives rise to intrinsic randomness. In an adversarial scenario, any additional degrees of freedom must be attributed to an eavesdropper with correlations to the measurement set-up. The true randomness…
Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs and their minimal defining…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
Since Renes et al. [J. Math. Phys. 45, 2171 (2004)], there has been much effort in the quantum information community to prove (or disprove) the existence of symmetric informationally complete (SIC) sets of quantum states in arbitrary finite…
We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal. Such a set is called a ``symmetric, informationally complete'' POVM (SIC-POVM) and is…
The L\"uders rule provides a way to define a quantum channel given a quantum measurement. Using this construction, we establish an if-and-only-if condition for the existence of a $d$-dimensional Symmetric Informationally Complete quantum…
Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite…
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
Symmetric informationally complete (SIC) POVMs are a class of quantum measurements which, in addition to being informationally complete, satisfy three conditions: 1) every POVM element is rank one, 2) the Hilbert-Schmidt inner product…
Symmetric informationally complete measurements are both important building blocks in many quantum information protocols and the seminal example of a generalised, non-orthogonal, quantum measurement. In higher-dimensional systems, these…
An unavoidable task in quantum information processing is how to obtain data about the state of an individual system by suitable measurements. Informationally complete measurements are relevant in quantum state tomography, quantum…
The accessible information quantifies the amount of classical information that can be extracted from an ensemble of quantum states. Analogously, the informational power quantifies the amount of classical information that can be extracted by…
Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC) positive operator-valued measurements (POVMs) are two related topics in quantum information theory. They are generalized to mutually unbiased measurements (MUMs)…