arXiv subjects

Sara Felloni

Publications and source records attributed to Sara Felloni.

5 recordsLinked to original sources

arXiv2009

Evolution of Quantum Systems by Diagrams of States

We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by quantum circuits. We present quantum diagrams of states for representations of quantum states by density matrices, partial trace operations, density matrix purification and time-evolution by Kraus operators. Following these representations, we describe by diagrams of states the most general transformations related to singlequbit decoherence and errors. Diagrams of states prove to be a useful approach to analyze quantum computations, by offering an intuitive graphic representation of the processing of quantum information. They also help in conceiving novel quantum computations, from describing the desired information processing to deriving the final implementation by quantum gate arrays.

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arXiv2009

An Error Model for the Cirac-Zoller CNOT gate

In the framework of ion-trap quantum computing, we develop a characterization of experimentally realistic imperfections which may affect the Cirac-Zoller implementation of the CNOT gate. The CNOT operation is performed by applying a protocol of five laser pulses of appropriate frequency and polarization. The laser-pulse protocol exploits auxiliary levels, and its imperfect implementation leads to unitary as well as non-unitary errors affecting the CNOT operation. We provide a characterization of such imperfections, which are physically realistic and have never been considered before to the best of our knowledge. Our characterization shows that imperfect laser pulses unavoidably cause a leak of information from the states which alone should be transformed by the ideal gate, into the ancillary states exploited by the experimental implementation.

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arXiv2009

Diagrams of States in Quantum Information: an Illustrative Tutorial

We present "Diagrams of States", a way to graphically represent and analyze how quantum information is elaborated during the execution of quantum circuits. This introductory tutorial illustrates the basics, providing useful examples of quantum computations: elementary operations in single-qubit, two-qubit and three-qubit systems, immersions of gates on higher dimensional spaces, generation of single and multi-qubit states, procedures to synthesize unitary, controlled and diagonal matrices. To perform the analysis of quantum processes, we directly derive diagrams of states from physical implementations of quantum circuits associated to the processes. Complete diagrams are then rearranged into simplified diagrams, to visualize the overall effects of computations. Conversely, diagrams of states help to conceive new quantum algorithms, by schematically describing desired manipulations of quantum information with intuitive diagrams and then by guessing the equivalent complete diagrams, from which the corresponding quantum circuit is obtained effortlessly. Related examples and analysis of complex algorithms will be provided in future works, for whose comprehension this first tutorial offers the necessary introduction.

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arXiv2006

A Graphic Representation of States for Quantum Copying Machines

The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear and detailed visualization of quantum information's flow during the unitary evolution of not too complex systems. The diagrams of states are exponentially more complex in respect to the standard representation and this clearly illustrates the discrepancy of computational power between quantum and classical systems. After a brief introductive exposure of the general theory, we present a constructive procedure to illustrate the new representation by means of concrete examples. Elementary diagrams of states for single-qubit and two-qubit systems and a simple scheme to represent entangled states are presented. Quantum copying machines as imperfect cloners of quantum states are introduced and the quantum copying machines of Griffiths and Niu and of Buzek and Hillery are analyzed, determining quantum circuits of easier interpretation. The method has indeed shown itself to be extremely successful for the representation of the involved quantum operations and it has allowed to point out the characteristic aspects of the quantum computations examined.

quant-ph↗

arXiv2005

Effects of single-qubit quantum noise on entanglement purification

We study the stability under quantum noise effects of the quantum privacy amplification protocol for the purification of entanglement in quantum cryptography. We assume that the E91 protocol is used by two communicating parties (Alice and Bob) and that the eavesdropper Eve uses the isotropic Bužek-Hillery quantum copying machine to extract information. Entanglement purification is then operated by Alice and Bob by means of the quantum privacy amplification protocol and we present a systematic numerical study of the impact of all possible single-qubit noise channels on this protocol. We find that both the qualitative behavior of the fidelity of the purified state as a function of the number of purification steps and the maximum level of noise that can be tolerated by the protocol strongly depend on the specific noise channel. These results provide valuable information for experimental implementations of the quantum privacy amplification protocol.

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