160 research outputs found
Strong quantitative benchmarking of quantum optical devices
Quantum communication devices, such as quantum repeaters, quantum memories,
or quantum channels, are unavoidably exposed to imperfections. However, the
presence of imperfections can be tolerated, as long as we can verify such
devices retain their quantum advantages. Benchmarks based on witnessing
entanglement have proven useful for verifying the true quantum nature of these
devices. The next challenge is to characterize how strongly a device is within
the quantum domain. We present a method, based on entanglement measures and
rigorous state truncation, which allows us to characterize the degree of
quantumness of optical devices. This method serves as a quantitative extension
to a large class of previously-known quantum benchmarks, requiring no
additional information beyond what is already used for the non-quantitative
benchmarks.Comment: 11 pages, 7 figures. Comments are welcome. ver 2: Improved figures,
no changes to main tex
Entanglement verification for quantum key distribution systems with an underlying bipartite qubit-mode structure
We consider entanglement detection for quantum key distribution systems that
use two signal states and continuous variable measurements. This problem can be
formulated as a separability problem in a qubit-mode system. To verify
entanglement, we introduce an object that combines the covariance matrix of the
mode with the density matrix of the qubit. We derive necessary separability
criteria for this scenario. These criteria can be readily evaluated using
semidefinite programming and we apply them to the specific quantum key
distribution protocol.Comment: 6 pages, 2 figures, v2: final versio
A reduced complexity numerical method for optimal gate synthesis
Although quantum computers have the potential to efficiently solve certain
problems considered difficult by known classical approaches, the design of a
quantum circuit remains computationally difficult. It is known that the optimal
gate design problem is equivalent to the solution of an associated optimal
control problem, the solution to which is also computationally intensive.
Hence, in this article, we introduce the application of a class of numerical
methods (termed the max-plus curse of dimensionality free techniques) that
determine the optimal control thereby synthesizing the desired unitary gate.
The application of this technique to quantum systems has a growth in complexity
that depends on the cardinality of the control set approximation rather than
the much larger growth with respect to spatial dimensions in approaches based
on gridding of the space, used in previous literature. This technique is
demonstrated by obtaining an approximate solution for the gate synthesis on
- a problem that is computationally intractable by grid based
approaches.Comment: 8 pages, 4 figure
One-way quantum key distribution: Simple upper bound on the secret key rate
We present a simple method to obtain an upper bound on the achievable secret
key rate in quantum key distribution (QKD) protocols that use only
unidirectional classical communication during the public-discussion phase. This
method is based on a necessary precondition for one-way secret key
distillation; the legitimate users need to prove that there exists no quantum
state having a symmetric extension that is compatible with the available
measurements results. The main advantage of the obtained upper bound is that it
can be formulated as a semidefinite program, which can be efficiently solved.
We illustrate our results by analysing two well-known qubit-based QKD
protocols: the four-state protocol and the six-state protocol. Recent results
by Renner et al., Phys. Rev. A 72, 012332 (2005), also show that the given
precondition is only necessary but not sufficient for unidirectional secret key
distillation.Comment: 11 pages, 1 figur
Optimal entanglement witnesses for continuous-variable systems
This paper is concerned with all tests for continuous-variable entanglement
that arise from linear combinations of second moments or variances of canonical
coordinates, as they are commonly used in experiments to detect entanglement.
All such tests for bi-partite and multi-partite entanglement correspond to
hyperplanes in the set of second moments. It is shown that all optimal tests,
those that are most robust against imperfections with respect to some figure of
merit for a given state, can be constructed from solutions to semi-definite
optimization problems. Moreover, we show that for each such test, referred to
as entanglement witness based on second moments, there is a one-to-one
correspondence between the witness and a stronger product criterion, which
amounts to a non-linear witness, based on the same measurements. This
generalizes the known product criteria. The presented tests are all applicable
also to non-Gaussian states. To provide a service to the community, we present
the documentation of two numerical routines, FULLYWIT and MULTIWIT, which have
been made publicly available.Comment: 14 pages LaTeX, 1 figure, presentation improved, references update
Chaotic Observer-based Synchronization Under Information Constraints
Limit possibilities of observer-based synchronization systems under
information constraints (limited information capacity of the coupling channel)
are evaluated. We give theoretical analysis for multi-dimensional
drive-response systems represented in the Lurie form (linear part plus
nonlinearity depending only on measurable outputs). It is shown that the upper
bound of the limit synchronization error (LSE) is proportional to the upper
bound of the transmission error. As a consequence, the upper and lower bounds
of LSE are proportional to the maximum rate of the coupling signal and
inversely proportional to the information transmission rate (channel capacity).
Optimality of the binary coding for coders with one-step memory is established.
The results are applied to synchronization of two chaotic Chua systems coupled
via a channel with limited capacity.Comment: 7 pages, 6 figures, 27 reference
Event-based security control for discrete-time stochastic systems
This study is concerned with the event-based security control problem for a class of discrete-time stochastic systems with multiplicative noises subject to both randomly occurring denial-of-service (DoS) attacks and randomly occurring deception attacks. An event-triggered mechanism is adopted with hope to reduce the communication burden, where the measurement signal is transmitted only when a certain triggering condition is violated. A novel attack model is proposed to reflect the randomly occurring behaviours of the DoS attacks as well as the deception attacks within a unified framework via two sets of Bernoulli distributed white sequences with known conditional probabilities. A new concept of mean-square security domain is put forward to quantify the security degree. The authors aim to design an output feedback controller such that the closed-loop system achieves the desired security. By using the stochastic analysis techniques, some sufficient conditions are established to guarantee the desired security requirement and the control gain is obtained by solving some linear matrix inequalities with nonlinear constraints. A simulation example is utilised to illustrate the usefulness of the proposed controller design scheme.This work was supported in part by Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61573246 and 61374039, the Shanghai Rising-Star Programme of China under Grant 16QA1403000, the Program for Capability Construction of Shanghai Provincial Universities under Grant 15550502500 and the Alexander von Humboldt Foundation of Germany
Truncated su(2) moment problem for spin and polarization states
We address the problem whether a given set of expectation values is
compatible with the first and second moments of the generic spin operators of a
system with total spin j. Those operators appear as the Stokes operator in
quantum optics, as well as the total angular momentum operators in the atomic
ensemble literature. We link this problem to a particular extension problem for
bipartite qubit states; this problem is closely related to the symmetric
extension problem that has recently drawn much attention in different contexts
of the quantum information literature. We are able to provide operational,
approximate solutions for every large spin numbers, and in fact the solution
becomes exact in the limiting case of infinite spin numbers. Solutions for low
spin numbers are formulated in terms of a hyperplane characterization, similar
to entanglement witnesses, that can be efficiently solved with semidefinite
programming.Comment: 18 pages, 1 figur
Algorithm Engineering in Robust Optimization
Robust optimization is a young and emerging field of research having received
a considerable increase of interest over the last decade. In this paper, we
argue that the the algorithm engineering methodology fits very well to the
field of robust optimization and yields a rewarding new perspective on both the
current state of research and open research directions.
To this end we go through the algorithm engineering cycle of design and
analysis of concepts, development and implementation of algorithms, and
theoretical and experimental evaluation. We show that many ideas of algorithm
engineering have already been applied in publications on robust optimization.
Most work on robust optimization is devoted to analysis of the concepts and the
development of algorithms, some papers deal with the evaluation of a particular
concept in case studies, and work on comparison of concepts just starts. What
is still a drawback in many papers on robustness is the missing link to include
the results of the experiments again in the design
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