Related papers: Unsharp measurements, joint measurability and clas…
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 density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…
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…
Quantum operations are used to describe the observed probability distributions and conditional states of the measured system. In this paper, we address the problem of their joint measurability (coexistence). We derive two equivalent…
We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) and a set of linearly independent post-measurement quantum states with a purely probabilistic representation of the Born Rule.…
Quantum uncertainty is described here in two guises: indeterminacy with its concomitant indeterminism of measurement outcomes, and fuzziness, or unsharpness. Both features were long seen as obstructions of experimental possibilities that…
The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys…
Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…
One of the peculiar features in quantum mechanics is that a superposition of macroscopically distinct states can exits. In optical system, this is highlighted by a superposition of coherent states (SCS), i.e. a superposition of classical…
The measurement problem in quantum mechanics originates in the inability of the Schr\"odinger equation to predict definite outcomes of measurements. This is due to the lack of objectivity of the eigenstates of the measuring apparatus. Such…
Quantum measurements can be interpreted as a generalisation of probability vectors, in which non-negative real numbers are replaced by positive semi-definite operators. We extrapolate this analogy to define a generalisation of doubly…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
We study the sample complexity of the classical shadows task: what is the fewest number of copies of an unknown state you need to measure to predict expected values with respect to some class of observables? Large joint measurements are…
Study of an N qubit mixed symmetric separable states is a long standing challenging problem as there exist no unique separability criterion. In this regard, we take up the N-qubit mixed symmetric separable states for a detailed study as…
Assuming a well-behaving quantum-to-classical transition, measuring large quantum systems should be highly informative with low measurement-induced disturbance, while the coupling between system and measurement apparatus is "fairly simple"…
A pair of orthonormal bases is called mutually unbiased if all mutual overlaps between any element of one basis with an arbitrary element of the other basis coincide. In case the dimension, $d$, of the considered Hilbert space is a power of…
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by…
We review the problem of state reconstruction in classical and in quantum physics, which is rarely considered at the textbook level. We review a method for retrieving a classical state in phase space, similar to that used in medical imaging…
We present the experimental quantum tomography of 7- and 8-dimensional quantum systems based on projective measurements in the mutually unbiased basis (MUB-QT). One of the advantages of MUB-QT is that it requires projections from a minimal…
Mutually unbiased bases encapsulate the concept of complementarity - the impossibility of simultaneous knowledge of certain observables - in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the…