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

Study of the Distillability of Werner States Using Entanglement Witnesses and Robust Semidefinite Programs

We use Robust Semidefinite Programs and Entanglement Witnesses to study the distillability of Werner states. We perform exact numerical calculations which show 2-undistillability in a region of the state space which was previously conjectured to be undistillable. We also introduce bases which yield interesting expressions for the {\em distillability witnesses} and for a tensor product of Werner states with arbitrary number of copies.Comment: 16 pages, 2 figure

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

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

Bell inequalities for three systems and arbitrarily many measurement outcomes

We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin Bell inequality. For a small number of outcomes, we verify that our inequalities define facets of the polytope of local correlations. We investigate the quantum violations of these inequalities, in particular with respect to the Hilbert space dimension. We provide strong evidence that the maximal quantum violation can only be reached using systems with local Hilbert space dimension exceeding the number of measurement outcomes. This suggests that our inequalities can be used as multipartite dimension witnesses.Comment: v1 6 pages, 4 tables; v2 Published version with minor typos correcte

Quantum benchmarking with realistic states of light

The goal of quantum benchmarking is to certify that imperfect quantum communication devices (e.g., quantum channels, quantum memories, quantum key distribution systems) can still be used for meaningful quantum communication. However, the test states used in quantum benchmarking experiments may be imperfect as well. Many quantum benchmarks are only valid for states which match some ideal form, such as pure states or Gaussian states. We outline how to perform quantum benchmarking using arbitrary states of light. We demonstrate these results using real data taken from a continuous-variable quantum memory.Comment: 14 pages, 3 figures. Updated to more closely match the published versio

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

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