Related papers: Quantum Reference Frames on Finite Homogeneous Spa…
The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a…
The purpose of quantum tomography is to determine an unknown quantum state from measurement outcome statistics. There are two obvious ways to generalize this setting. First, our task need not be the determination of any possible input state…
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…
Quantum reference frames are expected to differ from classical reference frames because they have to implement typical quantum features such as fluctuations and correlations. Here, we show that fluctuations and correlations of reference…
We discuss the concept of transformations among reference frames (classical or quantum). Usually transformations among classical reference frames have sharply defined parameters; geometrically they can be considered as {pure states in the…
We argue that correct account of the quantum properties of macroscopic objects which form reference frames (RF) demand the change of the standard space-time picture accepted in Quantum Mechanics. Galilean or Lorentz space-time…
We show that a rank-1 quantum observable (POVM) M is jointly measurable with a quantum observable M' exactly when M' is a smearing of M. If M is extreme, rank-1 and discrete then M and M' are coexistent if and only if they are jointly…
In recent years, quantum machine learning (QML) has been actively used for various tasks, e.g., classification, reinforcement learning, and adversarial learning. However, these QML studies are unable to carry out complex tasks due to…
Quantum Analogical Modeling (QAM) works under the assumption that the correct exemplar-based description for a system of behavior minimizes the overall uncertainty of the system. The measure used in QAM differs from the traditional…
Determining when the multiparameter quantum Cram\'er--Rao bound (QCRB) is saturable with experimentally relevant single-copy measurements is a central open problem in quantum metrology. Here we establish an equivalence between QCRB…
The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted…
This work is based on a description of quantum reference frames that seems more basic than others in the literature. Here a frame is based on a set of real and of complex numbers and a space time as a 4-tuple of the real numbers. There are…
In physical experiments, reference frames are standardly modelled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical…
The theory of decoherence attempts to explain the emergent classical behaviour of a quantum system interacting with its quantum environment. In order to formalize this mechanism we introduce the idea that the information preserved in an…
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…
The goal is to extend Gleason's notion of a frame function, which is essential in his fundamental theorem in quantum measurement, to a more general function acting on 1-tight, so-called, Parseval frames. We refer to these functions as…
Quantum communication without a shared reference frame or the construction of a relational quantum theory requires the notion of a quantum reference frame. We analyze aspects of quantum reference frames associated with non-compact groups,…
We propose a feasible experimental scheme to direct measure heat and work in cold atomic setups. The method is based on a recent proposal which shows that work is a positive operator valued measure (POVM). In the present contribution, we…
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…
Measurements on quantum channels are described by so-called process operator valued measures, or process POVMs. We study implementing schemes of extremal process POVMs. As it turns out, the corresponding measurement must satisfy certain…