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Stabilizer states are fundamental families of quantum states with crucial applications such as error correction, quantum computation, and simulation of quantum circuits. In this paper, we study the problem of testing how close or far a…
We introduce the notion of dismagicker: non-Clifford unitary gate designed to reduce the non-stabilizerness (also called magic) of quantum many-body states. Although both entanglement and non-stabilizerness are fundamental quantum…
Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially…
Random matrices tend to be well conditioned, and we employ this well known property to advance matrix computations. We prove that our algorithms employing Gaussian random matrices are efficient, but in our tests the algorithms have…
The effective description of a bosonic quantum system identifies the minimum finite dimension required to capture its essential dynamics. This effective dimension plays an important role in the complexity of classical and quantum algorithms…
The notion of partial trace of a density operator is essential for the understanding of the entanglement and separability properties of quantum states. In this paper we investigate these notions putting an emphasis on the geometrical…
Capturing the correlation emerging between constituents of many-body systems accurately is one of the key challenges for the appropriate description of various systems whose properties are underpinned by quantum mechanical fundamentals.…
We determine the optimal method of discriminating and comparing quantum states from a certain class of multimode Gaussian states and their mixtures when arbitrary global Gaussian operations and general Gaussian measurements are allowed. We…
A Gaussian elimination algorithm is presented that reveals the numerical rank of a matrix by yielding small entries in the Schur complement. The algorithm uses the maximum volume concept to find a square nonsingular submatrix of maximum…
Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical…
The dissipative dynamics of Gaussian squeezed states (GSS) and coherent superposition states (CSS) are analytically obtained and compared. Time scales for sustaining different quantum properties such as squeezing, negativity of the Wigner…
We characterize and classify quantum correlations in two-fermion systems having 2K single-particle states. For pure states we introduce the Slater decomposition and rank (in analogy to Schmidt decomposition and rank), i.e. we decompose the…
Advanced quantum technologies rely on non-Gaussian states of light, essential for universal quantum computation, fault-tolerant error correction, and quantum sensing. Their practical realization, however, faces hurdles: simulating large…
In this thesis we focus on Gaussian quantum metrology in the phase-space formalism and its applications in quantum sensing and the estimation of space-time parameters. We derive new formulae for the optimal estimation of multiple parameters…
We introduce a feasible protocol for generating non-Gaussian (nG) states via postselected von Neumann measurement for continuous-variable quantum information processing. The method uses a two-level system coupled to a Gaussian pointer state…
Gaussian quantum mechanics is a powerful tool regularly used in quantum optics to model linear and quadratic Hamiltonians efficiently. Recent interest in qubit-CV hybrid models has revealed a simple, yet important gap in our knowledge,…
We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semi-local Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical…
Groverian and Geometric entanglement measures of the n-party pure state are expressed by the (n-1)-party reduced state density operator directly. This main theorem derives several important consequences. First, if two pure n-qudit states…
We establish a link between stabilizer states, stabilizer rank, and higher-order Fourier analysis -- a still-developing area of mathematics that grew out of Gowers's celebrated Fourier-analytic proof of Szemer\'edi's theorem…
Quantum illumination is to discern the presence or absence of a low reflectivity target, where the error probability decays exponentially in the number of copies used. When the target reflectivity is small so that it is hard to distinguish…