arXiv subjects

Ernesto F. Galvao

Publications and source records attributed to Ernesto F. Galvao.

10 recordsLinked to original sources

arXiv2010

Closed timelike curves in measurement-based quantum computation

Many results have been recently obtained regarding the power of hypothetical closed time-like curves (CTCs) in quantum computation. Here we show that the one-way model of measurement-based quantum computation encompasses in a natural way the CTC model proposed by Bennett, Schumacher and Svetlichny. We identify a class of CTCs in this model that can be simulated deterministically and point to a fundamental limitation of Deutsch's CTC model which leads to predictions conflicting with those of the one-way model.

quant-ph↗

arXiv2009

Economical ontological models for discrete quantum systems

I use the recently proposed framework of ontological models [Harrigan et al., arXiv:0709.1149v2] to obtain economical models for results of tomographically complete sets of measurements on finite-dimensional quantum systems. I describe a procedure that simplifies the models by decreasing the number of necessary ontic states, and present an explicit model with just 33 ontic states for a qutrit.

quant-ph↗

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.

quant-ph↗

arXiv2005

Classicality in discrete Wigner functions

Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that the only pure states having non-negative W for all such functions are stabilizer states, as conjectured by one of us [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of W for all definitions of W form a subgroup of the Clifford group. This means pure states with non-negative W and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.

quant-ph↗

arXiv2005

Discrete Wigner functions and quantum computational speedup

In [Phys. Rev. A 70, 062101 (2004)] Gibbons et al. defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize a set C_d of states having non-negative W simultaneously in all definitions of W in this class. For d<6 I show C_d is the convex hull of stabilizer states. This supports the conjecture that negativity of W is necessary for exponential speedup in pure-state quantum computation.

quant-ph↗

arXiv2002

Foundations of quantum theory and quantum information applications

This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and non-locality, multipartite entanglement characterisation, and of a few quantum information protocols. Quantum non-locality and contextuality are shown to be essential for different implementations of quantum information protocols known as quantum random access codes and quantum communication complexity protocols. I derive sufficient experimental conditions for tests of these quantum properties. I also discuss how the distribution of quantum information through quantum cloning processes can be useful in quantum computing. Regarding entanglement characterisation, some results are obtained relating two problems, that of additivity of the relative entropy of entanglement, and that of identifying different types of tripartite entanglement in the asymptotic regime of manipulations of many copies of a given state. The thesis ends with a description of an information processing task in which a single qubit substitutes for an arbitrarily large amount of classical communication. This result is interpreted in different ways: as a gap between quantum and classical computation space complexity; as a bound on the amount of classical communication necessary to simulate entanglement; and as a basic result on hidden-variable theories for quantum mechanics. I also show that the advantage of quantum over classical communication can be established in a feasible experiment.

quant-ph↗

arXiv2002

Substituting a qubit for an arbitrarily large number of classical bits

We show that a qubit can be used to substitute for an arbitrarily large number of classical bits. We consider a physical system S interacting locally with a classical field phi(x) as it travels directly from point A to point B. The field has the property that its integrated value is an integer multiple of some constant. The problem is to determine whether the integer is odd or even. This task can be performed perfectly if S is a qubit. On the otherhand, if S is a classical system then we show that it must carry an arbitrarily large amount of classical information. We identify the physical reason for such a huge quantum advantage, and show that it also implies a large difference between the size of quantum and classical memories necessary for some computations. We also present a simple proof that no finite amount of one-way classical communication can perfectly simulate the effect of quantum entanglement.

quant-ph↗

arXiv2001

A feasible quantum communication complexity protocol

I show that a simple multi-party communication task can be performed more efficiently with quantum communication than with classical communication, even with low detection efficiency $η$. The task is a communication complexity problem in which distant parties need to compute a function of the distributed inputs, while minimizing the amount of communication between them. A realistic quantum optical setup is suggested that can demonstrate a five-party quantum protocol with higher-than-classical performance, provided $η>0.33$ .

quant-ph↗

arXiv2000

Experimental requirements for quantum communication complexity protocols

I present a simple two-party quantum communication complexity protocol with higher success rate than the best possible classical protocol for the same task. The quantum protocol is shown to be equivalent to a quantum non-locality test, except that it is not necessary to close the locality loophole. I derive bounds for the detector efficiency and background count rates necessary for an experimental implementation and show that they are close to what can be currently achieved using ion trap technology. I also analyze the requirements for a three-party protocol and show that they are less demanding than those for the two-party protocol. The results can be interpreted as sufficient experimental conditions for quantum non-locality tests using two or three entangled qubits.

quant-ph↗

arXiv2000

Cloning and quantum computation

We discuss how quantum information distribution can improve the performance of some quantum computation tasks. This distribution can be naturally implemented with different types of quantum cloning procedures. We give two examples of tasks for which cloning provides some enhancement in performance, and briefly discuss possible extensions of the idea.

quant-ph↗