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Quantum coherence is a fundamental feature of quantum mechanics and an underlying requirement for most quantum information tasks. In the resource theory of coherence, incoherent states are diagonal with respect to a fixed orthonormal basis,…
Generalized quantum measurements, described by positive operator-valued measures (POVMs), are essential for modeling realistic processes in open quantum systems. While quantum process tomography can fully characterize a POVM, it is…
We revisit the representation of generalized quantum observables by establishing a geometric picture in terms of their positive operator-valued measures (POVMs). This leads to a clear geometric interpretation of Born's rule by introducing…
Generalized quantum measurements (also known as POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform…
We construct relational observables in group field theory (GFT) in terms of covariant positive operator-valued measures (POVMs), using techniques developed in the context of quantum reference frames. We focus on matter quantum reference…
We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal POVM in the same von Neumann algebra. This generalizes to infinite dimension previous results in matrix algebras by…
We explain the powerful role that operator-valued measures can play in quantizing any set equipped with a measure, for instance a group (resp. group coset) with its invariant (resp. quasi-invariant) measure. Coherent state quantization is a…
Determining the conditions under which positive operator-valued measures (POVMs), the most general class of quantum measurements, outperform projective measurements remains a challenging and largely unresolved problem. Of particular…
The expectation value <O> of an arbitrary operator O can be obtained via a universal measuring apparatus that is independent of O, by changing only the data-processing of the outcomes. Such a ``universal detector'' performs a joint…
Constructing an integrated large-scale qubit system of realistic size requires addressing the challenge of physical crowding among qubits. This constraint poses an issue of coarse-grained (CG) measurement, wherein information from the…
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting…
Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalised positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a…
Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued…
This paper gives a brief introduction to Positive-Operator Valued Measure (POVM) of quantum communications. The Projection-Valued Measure (PVM) is first introduced and then the POVM. The relation between POVM and PVM is discussed and an…
In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the…
We consider how the theory of optimal quantum measurements determines the maximum information available to the receiving party of a quantum key distribution (QKD) system employing linearly independent but non-orthogonal quantum states. Such…
Symmetric informationally complete positive operator-valued measurement (SIC-POVM) is one important class of quantum measurement which is crucial for various quantum information processing tasks. SIC-POVMs have the advantage of providing an…
Generalized quantum measurements play a crucial role in quantum mechanics, and symmetric informationally complete positive operator-valued measurements (SIC POVMs) provide a powerful and flexible framework for extracting information from…
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…
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…