Related papers: Morphophoric POVMs, generalised qplexes, and 2-des…
We establish a general principle for the tomographic approach to quantum state reconstruction, till now based on a simple rotation transformation in the phase space, which allows us to consider other types of transformations. Then, we will…
In the previous parts of this work, we established the Prequantum Groupoid $\mathbf{T}_\omega$ as the universal geometric container for quantum mechanics. This approach, which we call the "Geometric Quantization by Paths" (GQbP) framework,…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
In this paper, we explore realist models of quantum theory that does not fit into the standard definitions of ontological models. The models here go beyond standard definition of ontological models in the sense that quantum states do not…
Informationally complete (IC) positive operator-valued measures (POVMs) are generalized quantum measurements that offer advantages over the standard computational basis readout of qubits. For instance, IC-POVMs enable efficient extraction…
The notion of Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) arose in physics as a kind of optimal measurement basis for quantum systems. However the question of their existence is equivalent to that of the…
This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…
The Measurement Based Quantum Computation (MBQC) model achieves universal quantum computation by employing projective single qubit measurements with classical feedforward on a highly entangled multipartite cluster state. Rapid advances in…
We consider graph states generated by the action of controlled phase shift operators on a separable state of a multi-qubit system. The case when all the qubits are initially prepared in arbitrary states is investigated. We obtain the…
Measurement-based quantum computation (MBQC) represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
Similarly to quantum states, also quantum measurements can be "mixed", corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely…
We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) and a set of linearly independent post-measurement quantum states with a purely probabilistic representation of the Born Rule.…
This paper presents a comprehensive perspective of the metric of quantum states with a focus on the background independent metric structures. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the…
Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation [M. Planat and Rukhsan-Ul-Haq, Preprint 1701.06443]. We show in this paper that a…
This investigation continues a program aiming at obtaining effective quantum models to describe measurement statistics. In [Stark, arXiv:1209.5737 (2012)], we have described how the Gram matrix associated to the prepared states and the…
Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random walks, while at the same time it allows for internal…
We report an experimental realization of adaptive Bayesian quantum state tomography for two-qubit states. Our implementation is based on the adaptive experimental design strategy proposed in [F.Husz\'ar and N.M.T.Houlsby, Phys.Rev.A 85,…
Can the state-space of $d$-dimensional quantum theory be derived from studying the behavior of a single "reference" measuring device? The answer is yes, if the measuring device corresponds to a complex-projective 3-design. In this…
We investigate the geometrical structure of multipartite states based on the construction of toric varieties. We show that the toric variety represents the space of general pure states and projective toric variety defines the space of…