arXiv subjects

Andrea Casaccino

Publications and source records attributed to Andrea Casaccino.

6 recordsLinked to original sources

arXiv2010

Entanglement manipulation via dynamics in multiple quantum spin systems

We study manipulation of entanglement between two identical networks of quantum mechanical particles. Firstly, we reduce the problem of entanglement transfer to the problem of quantum state transfer. Then, we consider entanglement concentration and purification based on free dynamics on the networks and local measurements on the vertices. By introducing an appropriate measure of efficiency, we characterize the performance of the protocol. We give evidence that such a measure does not depend on the network topology, and we estimate the contribution given by the number of entangled pairs initially shared by the two networks.

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arXiv2009

Quantum state transfer through a qubit network with energy shifts and fluctuations

We study quantum state transfer through a qubit network modeled by spins with XY interaction, when relying on a single excitation. We show that it is possible to achieve perfect transfer by shifting (adding) energy to specific vertices. This technique appears to be a potentially powerful tool to change, and in some cases improve, transfer capabilities of quantum networks. Analytical results are presented for all-to-all networks and all-to-all networks with a missing link. Moreover, we evaluate the effect of random fluctuations on the transmission fidelity.

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arXiv2008

Extrema of discrete Wigner functions and applications

We study the class of discrete Wigner functions proposed by Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] to describe quantum states using a discrete phase-space based on finite fields. We find the extrema of such functions for small Hilbert space dimensions, and present a quantum information application: a construction of quantum random access codes. These are constructed using the complete set of phase-space point operators to find encoding states and to obtain the codes' average success rates for Hilbert space dimensions 2,3,4,5,7 and 8.

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arXiv2008

Communication in XYZ All-to-All Quantum Networks with a Missing Link

We explicitate the relation between Hamiltonians for networks of interacting qubits in the XYZ model and graph Laplacians. We then study evolution in networks in which all sites can communicate with each other. These are modeled by the complete graph K_{n} and called all-to-all networks. It turns out that K_{n} does not exhibit perfect state transfer (PST). However, we prove that deleting an edge in K_{n} allows PST between the two non-adjacent sites, when n is a multiple of four. An application is routing a qubit over n different sites, by switching off the link between the sites that we wish to put in communication. Additionally, we observe that, in certain cases, the unitary inducing evolution in K_{n} is equivalent to the Grover operator.

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arXiv2008

An application of the Deutsch-Josza algorithm to formal languages and the word problem in groups

We adapt the Deutsch-Josza algorithm to the context of formal language theory. Specifically, we use the algorithm to distinguish between trivial and nontrivial words in groups given by finite presentations, under the promise that a word is of a certain type. This is done by extending the original algorithm to functions of arbitrary length binary output, with the introduction of a more general concept of parity. We provide examples in which properties of the algorithm allow to reduce the number of oracle queries with respect to the deterministic classical case. This has some consequences for the word problem in groups with a particular kind of presentation.

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arXiv2006

Quantum Error Correcting Subsystem Codes From Two Classical Linear Codes

The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most general method for encoding quantum information is to encode it into a subsystem, there exists a novel form of quantum error correction beyond the traditional quantum error correcting subspace codes. These new quantum error correcting subsystem codes differ from subspace codes in that their quantum correcting routines can be considerably simpler than related subspace codes. Here we present a class of quantum error correcting subsystem codes constructed from two classical linear codes. These codes are the subsystem versions of the quantum error correcting subspace codes which are generalizations of Shor's original quantum error correcting subspace codes. For every Shor-type code, the codes we present give a considerable savings in the number of stabilizer measurements needed in their error recovery routines.

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