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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…
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…
We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable positive operator valued measurement (POVM) on a finite number of…
We investigate a measure of quantum coherence and its extension to quantify quantum macroscopicity. The coherence measure can also quantify the asymmetry of a quantum state with respect to a given group transformation. We then show that a…
Wave packets for the Quantum Non-Linear Oscillator are considered in the Generalized Coherent State framerwork. To first order in the non-linearity parameter the Coherent State behaves very similarly to its classical counterpart. The…
While continuous-variable (CV) quantum systems are believed to be more efficient for quantum sensing and metrology than their discrete-variable (DV) counterparts due to the infinite spectrum of their native operators, our toolkit of…
The most general type of measurement in quantum physics is modeled by a positive operator-valued measure (POVM). Mathematically, a POVM is a generalization of a measure, whose values are not real numbers, but positive operators on a Hilbert…
Self-testing represents the strongest form of certification of a quantum system. Here we investigate theoretically and experimentally the question of self-testing non-projective quantum measurements. That is, how can one certify, from…
Considering some important classes of generalized coherent states known in literature, we demonstrated that all of them can be created via conventional fashion, i.e. the "lowering operator eigen-state" and the "displacement operator"…
Similarly to quantum states, also quantum measurements can be "mixed", corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely…
We consider the decoherence of a pseudo-spin ensemble under collective random rotations, and study, both theoretically and experimentally, how a nondestructive measurement combined with real-time feedback correction can protect the state…
We consider the convex set of positive operator valued measures (POVM) which are covariant under a finite dimensional unitary projective representation of a group. We derive a general characterization for the extremal points, and provide…
We investigate the presence of spin- and planar- squeezing in generalized superpositions of atomic (or spin) coherent states (ACS). Spin-squeezing has been shown to be a useful tool in determining the presence of entanglement in…
I give a first characterization of the class of generalized measurements that can be exactly realized on a pair of qudits encoded in indistinguishable particles, by using only linear elements and particle detectors. Two immediate results…
This work develops novel strategies for optimal planning with semantic observations using continuous state partially observable markov decision processes (CPOMDPs). Two major innovations are presented in relation to Gaussian mixture (GM)…
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
We introduce a generalization of symmetric measurements to collections of unequinumerous positive, operator-valued measures (POVMs). For informationally complete sets, we propose construction methods from orthonormal Hermitian operator…
Positive operator valued measurements on a finite number of N identically prepared systems of arbitrary spin J are discussed. Pure states are characterized in terms of Bloch-like vectors restricted by a SU(2 J+1) covariant constraint. This…
A theorem of Davies states that for symmetric quantum states there exists a symmetric POVM maximizing the mutual information. To apply this theorem the representation of the symmetry group has to be irreducible. We obtain a similar yet…
We propose a variational approach to the dynamics of the Bose-Hubbard model beyond the mean field approximation. To develop a numerical scheme, we use a discrete overcomplete set of Glauber coherent states and its connection to the…