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The article introduces efficient quantum state tomography schemes for qutrits and entangled qubits subject to pure decoherence. We implement the dynamic state reconstruction method for open systems sent through phase-damping channels which…
Establishing a notion of the quantum state that applies consistently across space and time could be a crucial step toward formulating a relativistic quantum theory. We give an operational meaning to multipartite quantum states over…
Quantum machine learning is a rapidly advancing discipline that leverages the features of quantum mechanics to enhance the performance of computational tasks. Quantum reservoir processing, which allows efficient optimization of a single…
We discuss the tomography of $N$-qubit states using collective measurements. The method is exact for symmetric states, whereas for not completely symmetric states the information accessible can be arranged as a mixture of irreducible SU(2)…
In this paper the problem of tomographic reconstruction of states is investigated within the so-called Schwinger's picture of Quantum Mechanics in which a groupoid is associated with every quantum system. The attention is focused on spin…
Copying information is an elementary operation in classical information processing. However, copying seems rather different in the quantum regime. Since the discovery of the universal quantum cloning machine, much has been found from the…
Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori unknown states can be completely determined…
We analyze the problem of reconstructing an unknown quantum state of a multipartite system from repeated measurements of local observables. In particular, via a system-theoretic observability analysis, we show that, even when the initial…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
Quantum coherence is the most fundamental feature of quantum mechanics. The usual understanding of it depends on the choice of the basis, that is, the coherence of the same quantum state is different within different reference framework. To…
Essential elements of quantum theory are derived from an epistemic point of view, i.e., the viewpoint that thetheory has to do with what can be said about nature. This gives a relationship to statistical reasoning and to other areas of…
High-dimensional quantum information processing has become a mature field of research with several different approaches being adopted for the encoding of $D$-dimensional quantum systems. Such progress has fueled the search of reliable…
Characterization of quantum states and devices is paramount to quantum science and technology. The characterization consists of individual measurements, which must be precisely known. A mismatch between actual and assumed constituent…
Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this…
Characterizing quantum systems is a fundamental task that enables the development of quantum technologies. Various approaches, ranging from full tomography to instances of classical shadows, have been proposed to this end. However, quantum…
Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known…
We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
A model of quantum measurement, illustrated using the spin--boson model, is formulated in terms of a cascading pair of quantum phase transitions. The first produces the desired superposition of macroscopic responses to the microscopic state…
We propose some new uses of toric variety structures in the study of quantum computation for small radices. In particular, we observe the concurrence of the equivalence classes of quantum states under quantum measurement and the orbits of…