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The quantum singular value transformation has revolutionised quantum algorithms. By applying a polynomial to an arbitrary matrix, it provides a unifying picture of quantum algorithms. However, polynomials are restricted to definite parity…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
We consider a protocol to perform the optimal quantum state discrimination of $N$ linearly independent non-orthogonal pure quantum states and present a computational code. Through the extension of the original Hilbert space, it is possible…
Consider a continuous time particle system $\eta^t=(\eta^t(k),k\in \mathbb{L})$, indexed by a lattice $\mathbb{L}$ which will be either $\mathbb{Z}$, $\mathbb{Z}/n\mathbb{Z}$, a segment $\{1,\cdots, n\}$, or $\mathbb{Z}^d$, and taking its…
The notion of convolution of two probability vectors, corresponding to a coincidence experiment can be extended for a family of binary operations determined by (tri)stochastic tensors, to describe Markov chains of a higher order. The…
Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behaviour and for its possible application in near-term quantum technologies. However, understanding these…
Continuous-time Markov decision processes are an important class of models in a wide range of applications, ranging from cyber-physical systems to synthetic biology. A central problem is how to devise a policy to control the system in order…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
Every year, substantial theoretical and experimental progress is made towards the realisation of a genuinely new computational paradigm in the construction of a quantum computer. But progress is fractal; to make headway is to unearth the…
Quantumness and separability criteria for continuous variable systems are discussed for the case of a noncommutative (NC) phase-space. In particular, the quantum nature and the entanglement configuration of NC two-mode Gaussian states are…
One of the core questions of quantum physics is how to reconcile the unitary evolution of quantum states, which is information-preserving and time-reversible, with evolution following the second law of thermodynamics, which, in general, is…
In conventional quantum mechanics the quantum particle is a special object, whose properties are described by special concepts and quantum principles. The quantization is a special procedure, which is accompanied by introduction of special…
Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable…
Currently, there is no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities. However, recent technological advances mean we have control over systems at scales where memory effects…
In recent years, much effort has been devoted to the construction of a proper measure of quantum non-Markovianity. However, those proposed measures are shown to be at variance with different situations. In this work, we utilize the theory…
In this paper, we study the problem of model-checking quantum pushdown systems from a computational complexity point of view. We arrive at the following equally important, interesting new results: We first extend the notions of the {\it…
The required set of operations for universal continuous-variable quantum computation can be divided into two primary categories: Gaussian and non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed as a sequence of…
In this paper, we continue the investigation of quantum Markov states (QMS) and define their mean entropies. Such entropies are explicitly computed under certain conditions. The present work takes a huge leap forward at tackling one of the…
We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We…
We formally extend the notion of Markov order to open quantum processes by accounting for the instruments used to probe the system of interest at different times. Our description recovers the classical Markov order property in the…