G. Lupieri’s research while affiliated with University of Milan and other places

... Our aim is to study a class of possible hybrid dynamics in the "Markov" case (no memory); so, we need to generalize quantum dynamical semigroups on the quantum side [8,15], and semigroups of transition probabilities on the classical side [16,17]. With respect to the theory of quantum measurements in continuous time, we are generalizing the notions of "convolution semigroups of instruments" and "semigroups of probability operators" [10][11][12][13][18][19][20][21][22][23][24][25]. ...

Reference:

Hybrid Quantum-Classical Systems: Quasi-Free Markovian Dynamics

... Corollary 2 may be regarded as a consequence of monotonicity, since any measurement with a countable set of outcomes can be framed as a CPTP G map given by Eq. (4.14), and by Corollary 1, the error cannot decrease. A POVM with a more general outcome space can still be framed as a quantum-classical channel; see, for example, Theorem 2 in Ref. [63], but it requires a mathematical framework far more complex than what is necessary for this work. An easier proof for general POVMs, to be presented in Appendix J, is to use a later result in Sec. 5. ...

Reference:

Operational meanings of a generalized conditional expectation in quantum metrology

... The relative entropy S(p q) is an informational quantity which is precisely tailored to quantify the amount of information that is lost by using an approximating probability q in place of the target one p. Although classical and quantum relative entropies have already been used in the evaluation of the performances of quantum measurements [24,27,30,[33][34][35][36][37][38][39][40], their first application to MURs is very recent [41]. ...

Reference:

Measurement Uncertainty Relations for Position and Momentum: Relative Entropy Formulation

... The theory of measurements continuous in time in quantum mechanics (quantum continual measurements) has been formulated by using the notions of instrument and positive operator valued measure [1]- [6] arisen inside the operational approach [1,7] to quantum mechanics, by using functional integrals [8,9,10], by using quantum stochastic differential equations [11]- [23] and by using classical stochastic differential equations (SDE's) [12]- [6]. Various types of SDE's are involved, and precisely linear and non linear equations for vectors in Hilbert spaces and for trace-class operators. ...

Reference:

Stochastic Differential Equations for Trace-Class Operators and Quantum Continual Measurements

... The interest in quantum/classical hybrid systems is old, see for instance [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein. One of the main motivations of the study of hybrid systems is that the output of a monitored system is classical; then, implicitly or explicitly, the dynamics of quantum/classical systems is involved in the theory of quantum measurements in continuous time and quantum filtering [1][2][3][4][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Moreover, hybrid systems could be used as an approximation to complicate quantum systems, as an effective theory [1,4,[9][10][11][12]29]. ...

Reference:

Markovian dynamics for a quantum/classical system and quantum trajectories

... Maccone [18] defined entropic disturbance and gave an upper bound on the maximum disturbance that a quantum state can undergo when information is being extracted from it. Barchielli and Lupieri [19] gave bounds on classical information gain by using positive-operator-valued measure (POVM)based measurements. Berta et al. [20] studied the information gain from a quantum measurement and showed the asymptotic simulation of quantum measurements using classical communication. ...

Reference:

Recovery from an eavesdropping attack on a qubit of a graph state

... In order to treat the two cases altogether, we consider POVMs with outcomes in R m × R m ≡ R 2m , which we call bi-observables; they correspond to a measurement of m position components and m momentum components. The specific covariance requirements will be given in the Definitions 5,6,7. In studying the properties of probability measures on R k , a very useful notion is that of the characteristic function, that is, the Fourier cotransform of the measure at hand; the analogous quantity for POVMs turns out to have the same relevance. ...

Reference:

Measurement Uncertainty Relations for Position and Momentum: Relative Entropy Formulation

... Under these conditions the associated dynamical semigroup (35) has been fully studied under the name of convolution semigroup of instruments and generalized to cases with a classical component not only in R s [27,46,[51][52][53][54][55][56]. In this construction a key point has been to exploit the analogies with the classical infinitely divisible distributions [44,45]. ...

Reference:

Markovian dynamics for a quantum/classical system and quantum trajectories

... Under these conditions the associated dynamical semigroup (35) has been fully studied under the name of convolution semigroup of instruments and generalized to cases with a classical component not only in R s [27,46,[51][52][53][54][55][56]. In this construction a key point has been to exploit the analogies with the classical infinitely divisible distributions [44,45]. ...

Reference:

Markovian dynamics for a quantum/classical system and quantum trajectories

... In quantum theory the notion of instrument [8] is introduced, which is a certain kind of operator-valued measure and allows to describe the results of a measurement (it gives probabilities and state changes). By using convolution semigroups of instruments it is possible to introduce certain quantum analogues of Markov processes, which describe measurements continuous in time [1,3,4,21]. ...

Reference:

A quantum analogue of Hunt's representation theorem for the generator of convolution semigroups on Lie groups