Massimiliano Federico Sacchi

Positive but not completely positive maps provide one of the most direct ways to detect entanglement beyond the positive-partial-transpose (PPT) criterion. We introduce and analyze an exactly solvable two-parameter family of sparse bistochastic positive maps on qutrits, in which two coherence channels are independently tuned by parameters w and z . The sparse structure makes the full phase diagram analytic: positivity holds exactly on the square 0 ≤ w , z ≤ 2 / 3 , complete positivity holds on the smaller square 0 ≤ w , z ≤ 1 / 3 , and decomposability is lost precisely outside a quarter circle in the corner w , z ≥ 1 / 3 . The indecomposable region is certified by explicit PPT entangled states adapted to the same witness geometry. At the end point W * = W ( 2 / 3 , 2 / 3 ) we construct a four-parameter family of PPT edge states of rank type (5,5), derive their analytic detection region, and show that the corresponding rays are exposed faces of the PPT cone. Finally, although W * is not optimal, we give an explicit optimal refinement whose detection region on this family is strictly larger. The result is an analytically tractable qutrit setting in which positivity, indecomposability, PPT entanglement, optimality, and exposed convex geometry can be studied in a single framework.

We determine the optimal information-disturbance tradeoff for estimating an unknown spatial direction encoded in two antiparallel spins. Rotational covariance reduces the optimization over all instruments to a finite-dimensional Choi problem: a positive seed operator obeys one trace constraint for each irreducible sector of the input representation, while both the directional score and the operation fidelity are linear functionals of this seed. For two antiparallel spin- 1 / 2 particles, whose physical representation decomposes as 0 ⊕ 1 , we derive the two-multiplier dual problem and characterize the optimal instrument from the kernel vectors of the dual slack operator. The optimal operation is a covariant filter with scalar-vector coherence and is generally not a convex interpolation between the identity channel and a measure-and-reprepare strategy. At maximum information, we recover the Gisin-Popescu score, but the least disturbing output state is optimized independently, giving a smaller disturbance than both the parallel-spin benchmark and antiparallel measure-and-reprepare. We also formulate the parallel benchmark and, as a central extension of the method, treat antiparallel spin-coherent states of arbitrary spin j . In this case the signal coherently occupies all sectors ℓ = 0 , ... , 2 j of j ⊗ j , the endpoint information is governed by nearest-neighbor sector coherences, and the endpoint disturbance is obtained from an explicit finite block-diagonal eigenvalue problem.

Time-varying quantum channels are essential for modeling realistic quantum systems with evolving noise properties. Here, we consider Gaussian lossy channels varying from one use to another and we employ neural networks to classify, regress, and forecast the behavior of these channels from their Choi-Jamiołkowski states. The networks achieve at least 87% of accuracy in distinguishing between non-Markovian, Markovian, memoryless, compound, and deterministic channels. In regression tasks, the model accurately reconstructs the loss parameter sequences, and in forecasting, it predicts future values, with improved performance as the memory parameter approaches 1 for Markovian channels. These results demonstrate the potential of neural networks in characterizing and predicting the dynamics of quantum channels.

We study the thermodynamics of two-stroke heat engines where two bosonic modes a and b are coupled by the general nonlinear interaction V θ = exp ⁡ ( θ a † n b m − θ ∗ a n b † m ) . By adopting the two-point measurement scheme we retrieve the distribution of the stochastic work, and hence the relative fluctuations of the extracted work up to the second order in the coupling θ. We identify the optimal interactions providing large average work with small fluctuations in the operational regime of the heat engine. Then, we consider the specific cases n = 2, m = 1 and n = 1, m = 2 up to the fourth order in θ. We optimize the average work and the signal-to-noise ratio over the frequencies of the bosonic modes and the temperatures of the reservoirs. Finally, we determine the thermodynamic uncertainty relations for these processes in relation with the order of the expansion of the unitary interaction V _θ .

We present a novel methodology utilizing recurrent neural networks (RNNs) to classify Markovian and non-Markovian quantum processes, leveraging time series data derived from Choi states. The model exhibits exceptional accuracy, surpassing 95%, across diverse scenarios, including dephasing and Pauli channels in an arbitrary basis, generalized amplitude damping dynamics, and even in the presence of noise. Additionally, the developed model shows efficient forecasting capabilities for the analyzed time series data. These results suggest the potential of RNNs in discerning and predicting the Markovian nature of quantum processes.

We study the work fluctuations in ergotropic heat engines, namely two-stroke quantum Otto engines where the work stroke is designed to extract the ergotropy (the maximum amount of work by a cyclic unitary evolution) from a couple of quantum systems at canonical equilibrium at two different temperatures, whereas the heat stroke thermalizes back the systems to their respective reservoirs. We provide an exhaustive study for the case of two qutrits whose energy levels are equally spaced at two different frequencies by deriving the complete work statistics. By varying the values of temperatures and frequencies, only three kinds of optimal unitary strokes are found: the swap operator U1, an idle swap U2 (where one of the qutrits is regarded as an effective qubit), and a non-trivial permutation of energy eigenstates U3, which indeed corresponds to the composition of the two previous unitaries, namely U3=U2U1. While U1 and U2 are Hermitian (and hence involutions), U3 is not. This point has an impact on the thermodynamic uncertainty relations (TURs), which bound the signal-to-noise ratio of the extracted work in terms of the entropy production. In fact, we show that all TURs derived from a strong detailed fluctuation theorem are violated by the transformation U3.

We study the work fluctuations in ergotropic heat engines, namely two-strokes quantum Otto engines where the work stroke is designed to extract the ergotropy (the maximum amount of work by a cyclic unitary evolution) from a couple of quantum systems at canonical equilibrium at two different temperatures, whereas the heat stroke thermalizes back the systems to their respective reservoirs. We provide an exaustive study for the case of two qutrits whose energy levels are equally spaced at two different frequencies by deriving the complete work statistics. By varying the values of temperatures and frequencies, only three kinds of optimal unitary strokes are found: the swap operator U1, an idle swap U2 (where one of the qutrits is regarded as an effective qubit), and a non trivial permutation of energy eigenstates U3, which indeed corresponds to the composition of the two previous unitaries, namely U3 = U2U1. While U1 and U2 are Hermitian (and hence involutions), U3 is not. This point has an impact on the thermodynamic uncertainty relations (TURs) which bound the signal-to-noise ratio of the extracted work in terms of the entropy production. In fact, we show that all TURs derived from a strong detailed fluctuation theorem are violated by the transformation U3.

We study energetic exchanges and fluctuations in two-stroke quantum thermodynamic engines where the working fluid is represented by two multilevel quantum systems, i.e., qudits, the heat flow is allowed by relaxation with two thermal reservoirs at different temperatures, and the work exchange is operated by a partial-swap unitary interaction. We identify three regimes of operation (heat engine, refrigerator, and thermal accelerator), present the thermodynamic uncertainty relations between the entropy production and the signal-to-noise ratio of work and heat, and derive the full joint probability of the stochastic work and heat. Our results bridge the gap between two-qubit and two-mode bosonic swap engines, and show which properties are maintained (e.g., a nonfluctuating Otto efficiency) and which are lost for increasing dimension (e.g., small violations of the standard thermodynamic uncertainty relations or the possibility of beating the Curzon-Ahlborn efficiency).