141,757 research outputs found
Quantum-enhanced multi-parameter estimation for unitary photonic systems
Precise device characterization is a fundamental requirement for a large
range of applications using photonic hardware, and constitutes a
multi-parameter estimation problem. Estimates based on measurements using
single photons or classical light have precision which is limited by
shot-noise, while quantum resources can be used to achieve sub-shot-noise
precision. However, there are many open questions with regard to the best
quantum protocols for multi-parameter estimation, including the ultimate limits
to achievable precision, as well as optimal choices for probe states and
measurements. In this paper, we develop a formalism based on Fisher information
to tackle these questions for set-ups based on linear-optical components and
photon-counting measurements. A key ingredient of our analysis is a mapping for
equivalent protocols defined for photonic and spin systems, which allows us to
draw upon results in the literature for general finite-dimensional systems.
Motivated by the protocol in X.-Q. Zhou, et al., Optica 2, 510 (2015), we
present new results for quantum-enhanced tomography of unitary processes,
including a comparison of Holland-Burnett and NOON probe states.Comment: 19 pages, 6 figure
Designing Network Protocols for Good Equilibria
Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network cost-sharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal cost-sharing protocols for undirected and directed graphs, single-sink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the cost-sharing protocols that induce only network games with pure-strategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs
Coded Cooperative Data Exchange for a Secret Key
We consider a coded cooperative data exchange problem with the goal of
generating a secret key. Specifically, we investigate the number of public
transmissions required for a set of clients to agree on a secret key with
probability one, subject to the constraint that it remains private from an
eavesdropper.
Although the problems are closely related, we prove that secret key
generation with fewest number of linear transmissions is NP-hard, while it is
known that the analogous problem in traditional cooperative data exchange can
be solved in polynomial time. In doing this, we completely characterize the
best possible performance of linear coding schemes, and also prove that linear
codes can be strictly suboptimal. Finally, we extend the single-key results to
characterize the minimum number of public transmissions required to generate a
desired integer number of statistically independent secret keys.Comment: Full version of a paper that appeared at ISIT 2014. 19 pages, 2
figure
Secret Key Agreement from Correlated Gaussian Sources by Rate Limited Public Communication
We investigate the secret key agreement from correlated Gaussian sources in
which the legitimate parties can use the public communication with limited
rate. For the class of protocols with the one-way public communication, we show
a closed form expression of the optimal trade-off between the rate of key
generation and the rate of the public communication. Our results clarify an
essential difference between the key agreement from discrete sources and that
from continuous sources.Comment: 9 pages, no figure, Version 2 is a published version. The results are
not changed from version 1. Explanations are polishe
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