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Petra F. Scudo

Publications and source records attributed to Petra F. Scudo.

12 recordsLinked to original sources

Geometrical derivation of Wigner's angle for arbitrary Lorentz transformations of massless particles

This note summarizes the physics and mathematics of Lorentz transformations for massless particles, specifically for photons. We provide a complete analytical derivation of Wigner's little group matrix and a closed formula for the calculation of Wigner's angle for arbitrary Lorentz transformations. Our derivation highlights the geometrical content of the sequence of little group transformations leading to Wigner's matrix and links it to classical theorems in spherical trigonometry.

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Can optimal collective measurements outperform individual measurements for non-orthogonal QKD signals?

We consider how the theory of optimal quantum measurements determines the maximum information available to the receiving party of a quantum key distribution (QKD) system employing linearly independent but non-orthogonal quantum states. Such a setting is characteristic of several practical QKD protocols. Due to non-orthogonality, the receiver is not able to discriminate unambiguously between the signals. To understand the fundamental limits that this imposes, the quantity of interest is the maximum mutual information between the transmitter (Alice) and the receiver, whether legitimate (Bob) or an eavesdropper (Eve). To find the optimal measurement we use a framework based on operator algebra and general results derived from singular value decomposition, achieving optimal solutions for von Neumann measurements and positive operator-valued measures (POVMs). The formal proof and quantitative analysis elaborated for two signals allow one to conclude that optimal von Neumann measurements are uniquely defined and provide a higher information gain compared to POVMs. Interestingly, collective measurements not only do not provide additional information gain with respect to individual ones, but also suffer from a gain reduction in the case of POVMs.

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Quantum communications infrastructure architecture: theoretical background, network structure and technologies. A review of recent studies from a European public infrastructure perspective

Progress in the development of techniques for the construction of multiuser quantum communications networks is reviewed in light of the plans for an EU quantum communications infrastructure (EU QCI). Quantum key distribution networks may be classified as trusted node; quantum repeater-entanglement-swapping based; point-to-multipoint based on passive beam splitters, active optical switchers or WDM; high dimensional-multipartite entanglement and flexible reconfigurable multipartite networks. Both satellite and terrestrial implementations are possible and ore both planned for EU QCI; their relative merits are discussed. Current technology falls short in several respects of what is required to address use cases well. Bit rates as a function of distance are currently limited by the characteristics of available devices and are an order of magnitude or more below the theoretical bounds. Non-ideal device behaviour can open loopholes for side-channel attacks. Limited range constrains network geometry. New techniques are being developed to overcome these problems. The more sophisticated schemes depend on ongoing advances in the generation and distribution of entanglement. Particularly promising are the measurement device independent protocol, which eliminates photon-detector related security weaknesses, and the twin-field protocol, which uses similar techniques to extend range, in principle even beyond previously accepted theoretical bounds. Agreement of keys between more than two users can be accomplished classically after pairwise quantum key exchange but direct quantum multipartite agreement using may offer advantages. The same applies to secret sharing. Practical quantum repeaters, to eliminate the need for trusted nodes, are closer to being realised due to recent progress in optical memories.

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Spectral converters and luminescent solar concentrators

In this paper we present a comprehensive theoretical description of molecular spectral converters in the specific context of Luminescent Solar Concentrators (LSCs). The theoretical model is an extension to a three-level system interacting with a solar radiation bath of the standard quantum theory of atomic radiative processes. We derive the equilibrium equations of the conversion process and provide specific examples of application of this principle to the development of solar concentration devices.

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Quantum estimation of relative information

We derive optimal schemes for preparation and estimation of relational degrees of freedom between two quantum systems. We specifically analyze the case of rotation parameters representing relative angles between elements of the SU(2) symmetry group. Our estimation procedure does not assume prior knowledge of the absolute spatial orientation of the systems and as such does not require information on the underlying classical reference frame in which the states are prepared.

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Convergence of coined quantum walks on d-dimensional Euclidean space

Coined quantum walks may be interpreted as the motion in position space of a quantum particle with a spin degree of freedom; the dynamics are determined by iterating a unitary transformation which is the product of a spin transformation and a translation conditional on the spin state. Coined quantum walks on the d-dimensional lattice can be treated as special cases of coined quantum walks on d-dimensional Euclidean space. We study quantum walks on d-dimensional Euclidean space and prove that the sequence of rescaled probability distributions in position space associated to the unitary evolution of the particle converges to a limit distribution.

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A de Finetti Representation Theorem for Quantum Process Tomography

In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for probability distributions, we give a definition of exchangeability for sequences of quantum operations. We then state and prove a representation theorem for such exchangeable sequences. The theorem leads to a simple characterization of admissible priors for quantum process tomography and solves to a Bayesian's satisfaction the problem of an unknown quantum operation.

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Quantum entropy and special relativity

We consider a single free spin 1/2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.

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Unspeakable quantum information

No verbal explanation can indicate a direction in space or the orientation of a coordinate system. Only material objects can do it. In this article we consider the use of a set of spin-\half particles in an entangled state for indicating a direction, or a hydrogen atom in a Rydberg state for transmitting a Cartesian frame. Optimal strategies are derived for the emission and detection of the quantum signals.

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Covariant quantum measurements may not be optimal

Quantum particles, such as spins, can be used for communicating spatial directions to observers who share no common coordinate frame. We show that if the emitter's signals are the orbit of a group, then the optimal detection method may not be a covariant measurement (contrary to widespread belief). It may be advantageous for the receiver to use a different group and an indirect estimation method: first, an ordinary measurement supplies redundant numerical parameters; the latter are then used for a nonlinear optimal identification of the signal.

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Transmission of a Cartesian Frame by a Quantum System

A single quantum system, such as a hydrogen atom, can transmit a Cartesian coordinate frame (three axes). For this it has to be prepared in a superposition of states belonging to different irreducible representations of the rotation group. The algorithm for decoding such a state is presented, and the fidelity of transmission is evaluated.

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Entangled quantum states as direction indicators

We consider the use of N spin-1/2 particles for indicating a direction in space. If N>2, their optimal state is entangled. For large N, the mean square error decreases as N^{-2} (rather than N^{-1} for parallel spins).

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