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We present adaptive measurement techniques tailored for variational quantum algorithms on near-term small and noisy devices. In particular, we generalise earlier "learning to measure" strategies in two ways. First, by considering a class of…
We study generalized measurements (POVM measurements) on a single d-level quantum system which is in a completely unknown pure state, and derive the best estimate of the post-measurement state. The mean post-measuremement estimation…
Manipulation of qudits in optical tables is a difficult and nonscalable task. The use of integrated optical circuits opens new possibilities for the generation, manipulation, and characterization of high dimensional states besides the ease…
When measuring phase of quantum states of light, the optimal single-shot measurement implements projection on the un-physical phase states. If we want to improve the precision further we need to accept a reduced probability of success,…
In this paper we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can…
We apply algorithmic information theory to quantum mechanics in order to shed light on an algorithmic structure which inheres in quantum mechanics. There are two equivalent ways to define the (classical) Kolmogorov complexity K(s) of a…
We consider the convex sets of QO's (quantum operations) and POVM's (positive operator valued measures) which are covariant under a general finite-dimensional unitary representation of a group. We derive necessary and sufficient conditions…
We address the problem of estimating the phase phi given N copies of the phase rotation u(phi) within an array of quantum operations in finite dimensions. We first consider the special case where the array consists of an arbitrary input…
Performing perfect/conclusive quantum state exclusion means to be able to discard with certainty at least one out of n possible quantum state preparations by performing a measurement of the resulting state. This task of state exclusion has…
It is well-known in classical frame theory that overcomplete representations of a given vector space provide robustness to additive noise on the frame coefficients of an unknown vector. We describe how the same robustness can be shown to…
We investigate four partial orderings on the space of quantum measurements (i.e on POVMs or positive operator valued measures), describing four notions of coarse/fine-ness of measurement. These are the partial orderings induced by: (1)…
We derive the class of covariant measurements which are optimal according to the maximum likelihood criterion. The optimization problem is fully resolved in the case of pure input states, under the physically meaningful hypotheses of…
Consider a spin s prepared in a pure state. It is shown that, generically, the moduli of the (2s+1) spin components along three directions in space determine the state unambiguously. These probabilities are accessible experimentally by…
Efficiently extracting information from pure quantum states using minimal observables on the main system is a longstanding and fundamental issue in quantum information theory. Despite the inability of probability distributions of position…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the…
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different…
We introduce a new method to estimate unknown pure $d$-dimensional quantum states using the probability distributions associated with only three measurement bases. Measurement results of $2d$ projectors are employed to generate a set of…
Quantum state tomography (QST) remains the gold standard for benchmarking and verification of near-term quantum devices. While QST for a generic quantum many-body state requires an exponentially large amount of resources, most physical…
The goal of comparison is to reveal the difference of compared objects as fast and reliably as possible. In this paper we formulate and investigate the unambiguous comparison of unknown quantum measurements represented by non-degenerate…
The concept of intrinsic and operational observables in quantum mechanics is introduced. It is argued that, in any realistic description of a quantum measurement that includes a detecting device, it is possible to construct from the…