arXiv subjects

Gerardo A. Paz-Silva

Publications and source records attributed to Gerardo A. Paz-Silva.

25 records · Page 2Linked to original sources

arXiv2013

Analysis of the quantum Zeno effect for quantum control and computation

Within quantum information, many methods have been proposed to avoid or correct the deleterious effects of the environment on a system of interest. In this work, expanding on our earlier paper [G. A. Paz-Silva et al., Phys. Rev. Lett. 108, 080501 (2012), arXiv:1104.5507], we evaluate the applicability of the quantum Zeno effect as one such method. Using the algebraic structure of stabilizer quantum error correction codes as a unifying framework, two open-loop protocols are described which involve frequent non-projective (i.e., weak) measurement of either the full stabilizer group or a minimal generating set thereof. The effectiveness of the protocols is measured by the distance between the final state under the protocol and the final state of an idealized evolution in which system and environment do not interact. Rigorous bounds on this metric are derived which demonstrate that, under certain assumptions, a Zeno effect may be realized with arbitrarily weak measurements, and that this effect can protect an arbitrary, unknown encoded state against the environment arbitrarily well.

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arXiv2010

Full Additivity of the Entanglement of Formation

We present a general strategy that allows a more flexible method for the construction of fully additive multipartite entanglement monotones than the ones so far reported in the literature of axiomatic entanglement measures. Within this framework we give a proof of a conjecture of outstanding implications in information theory: the full additivity of the Entanglement of Formation.

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arXiv2010

On fault-tolerance with noisy and slow measurements

It is not so well-known that measurement-free quantum error correction protocols can be designed to achieve fault-tolerant quantum computing. Despite the potential advantages of using such protocols in terms of the relaxation of accuracy, speed and addressing requirements on the measurement process, they have usually been overlooked because they are expected to yield a very bad threshold as compared to error correction protocols which use measurements. Here we show that this is not the case. We design fault-tolerant circuits for the 9 qubit Bacon-Shor code and find a threshold for gates and preparation of $p_{(p,g) thresh}=3.76 \times 10^{-5}$ (30% of the best known result for the same code using measurement based error correction) while admitting up to 1/3 error rates for measurements and allocating no constraints on measurement speed. We further show that demanding gate error rates sufficiently below the threshold one can improve the preparation threshold to $p_{(p)thresh} = 1/3$. We also show how these techniques can be adapted to other Calderbank-Shor-Steane codes.

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arXiv2009

Geometric multipartite entanglement measures

Within the framework of constructions for quantifying entanglement, we build a natural scenario for the assembly of multipartite entanglement measures based on Hopf bundle-like mappings obtained through Clifford algebra representations. Then, given the non-factorizability of an arbitrary two-qubit density matrix, we give an alternate quantity that allows the construction of two types of entanglement measures based on their arithmetical and geometrical averages over all pairs of qubits in a register of size N, and thus fully characterize its degree and type of entanglement. We find that such an arithmetical average is both additive and strongly super additive.

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arXiv2009

Perfect mirror transport protocol with higher dimensional quantum chains

A globally controlled scheme for quantum transport is proposed. The scheme works on a 1D chain of nearest neighbor coupled systems of qudits (finite dimension), or qunats (continuous variable), taking any arbitrary initial quantum state of the chain and producing a final quantum state which is perfectly spatially mirrored about the mid-point of the chain. As a particular novel application, the method can be used to transport continuous variable (CV) quantum states. A physical realization is proposed where it is shown how the quantum states of the microwave fields held in a chain of driven superconducting coplanar waveguides can experience quantum mirror transport when coupled by switchable Cooper Pair Boxes.

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arXiv2007

Total correlations as fully additive entanglement monotones

We generalize the strategy presented in Refs. [1, 2], and propose general conditions for a measure of total correlations to be an entanglement monotone using its pure (and mixed) convex-roof extension. In so doing, we derive crucial theorems and propose a concrete candidate for a total correlations measure which is a fully additive entanglement monotone.

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arXiv2007

A pairwise additive strategy for quantifying multipartite entanglement

Based on the idea of measuring the factorizability of a given density matrix, we propose a pairwise analysis strategy for quantifying and understanding multipartite entanglement. The methodology proves very effective as it immediately guarantees, in addition to the usual entanglement properties, additivity and strong super additivity. We give a specific set of quantities that fulfill the protocol and which, according to our numerical calculations, make the entanglement measure an LOCC non-increasing function. The strategy allows a redefinition of the structural concept of global entanglement.

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