Related papers: Equivalence relations between conical 2-designs an…
Quantum coherence with respect to orthonormal bases has been studied extensively in the past few years. Recently, Bischof, et al. [Phys. Rev. Lett. 123, 110402 (2019)] generalized it to the case of general positive operator-valued measure…
From an operational point of view, we propose several new entanglement detection criteria using quantum designs. These criteria are constructed by considering the correlations defined with quantum designs. Counter-intuitively, the criteria…
Loss induced generalized measurements have been introduced years ago as a mean to implement generalized quantum measurements (POVM). Here the original idea is extended to a complete equivalence of lossy evolution and a certain widely used…
We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These…
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…
Measurements in quantum theory exhibit incompatibility, i.e., they can fail to be jointly measurable. An intuitive way to represent the (in)compatibility relations among a set of measurements is via a hypergraph representing their joint…
In this paper, we establish a connection between zonoids (a concept from classical convex geometry) and the distinguishability norms associated to quantum measurements, or POVMs (Positive Operator-Valued Measures), recently introduced in…
While quantum correlations between two spacelike-separated systems are fully encoded by the bipartite density operator associated with the joint system, there does not exist an analogous operator representing general quantum correlations…
The thesis is mainly about the construction and implementation of cyclic mutually unbiased bases, dealing with different entanglement structures by discussing the related group structures. A recursive construction for Fermat number…
We derive expressions for the invariant length element and measure for the simple compact Lie group SU(4) in a coordinate system particularly suitable for treating entanglement in quantum information processing. Using this metric, we…
Even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols they remain ill understood. Here, we construct special sets of up to 2n+1 mutually unbiased bases (MUBs) in…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
The objective of this work is to develop a recursive, discrete time quantum filtering equation for a system that interacts with a probe, on which measurements are performed according to the Positive Operator Valued Measures (POVMs)…
Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it connects distinct theories and also reveals hidden structures in a given theory. We initiate a systematic investigation of gauging discrete generalized…
This short note highlights the most prominent mathematical problems and physical questions associated with the existence of the maximum sets of mutually unbiased bases (MUBs) in the Hilbert space of a given dimension
We consider the implementation of a symmetric informationally complete probability-operator measurement (SIC POM) in the Hilbert space of a d-level system by a two-step measurement process: a diagonal-operator measurement with high-rank…
Accurate characterisation of two-qubit gates will be critical for any realisation of quantum computation. We discuss a range of measurements aimed at characterising a two-qubit gate, specifically the CNOT gate. These measurements are…
The relation between projective measurements and generalized quantum measurements is a fundamental problem in quantum physics, and clarifying this issue is also important to quantum technologies. While it has been intuitively known that…
Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation [M. Planat and Rukhsan-Ul-Haq, Preprint 1701.06443]. We show in this paper that a…
One of the essential features of quantum mechanics is that most pairs of observables cannot be measured simultaneously. This phenomenon is most strongly manifested when observables are related to mutually unbiased bases. In this paper, we…