arXiv subjects

Norbert Lütkenhaus

Publications and source records attributed to Norbert Lütkenhaus.

At least 109 records · Page 6Linked to original sources

arXiv2008

Iterations of nonlinear entanglement witnesses

We describe a generic way to improve a given linear entanglement witness by a quadratic, nonlinear term. This method can be iterated, leading to a whole sequence of nonlinear witnesses, which become stronger in each step of the iteration. We show how to optimize this iteration with respect to a given state, and prove that in the limit of the iteration the nonlinear witness detects all states that can be detected by the positive map corresponding to the original linear witness.

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arXiv2008

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.

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arXiv2008

Testing Quantum Devices: Practical Entanglement Verification in Bipartite Optical Systems

We present a method to test quantum behavior of quantum information processing devices, such as quantum memories, teleportation devices, channels and quantum key distribution protocols. The test of quantum behavior can be phrased as the verification of effective entanglement. Necessary separability criteria are formulated in terms of a matrix of expectation values in conjunction with the partial transposition map. Our method is designed to reduce the resources for entanglement verification. A particular protocol based on coherent states and homodyne detection is used to illustrate the method. A possible test for the quantum nature of memories using two non-orthogonal signal states arises naturally. Furthermore, closer inspection of the measurement process in terms of the Stokes operators reveals a security threat for quantum key distribution involving phase reference beams.

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arXiv2007

Optimal unambiguous state discrimination of two density matrices: A second class of exact solutions

We consider the Unambiguous State Discrimination (USD) of two mixed quantum states. We study the rank and the spectrum of the elements of an optimal USD measurement. This naturally leads to a partial fourth reduction theorem. This theorem shows that either the failure probability equals its overall lower bound given in term of the fidelity or a two-dimensional subspace can be split off from the original Hilbert space. We then use this partial reduction theorem to derive the optimal solution for any two equally probable Geometrically Uniform (GU) states $ρ_0$ and $ρ_1=Uρ_0 U^\dagger$, $U^2={\openone}$, in a four-dimensional Hilbert space. This represents a second class of analytical solutions for USD problems that cannot be reduced to some pure state cases. We apply our result to answer two questions that are relevant in implementations of the Bennett and Brassard 1984 quantum key distribution protocol using weak coherent states.

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arXiv2007

Security of coherent state quantum cryptography in the presence of Gaussian noise

We investigate the security against collective attacks of a continuous variable quantum key distribution scheme in the asymptotic key limit for a realistic setting. The quantum channel connecting the two honest parties is assumed to be lossy and imposes Gaussian noise on the observed quadrature distributions. Secret key rates are given for direct and reverse reconciliation schemes including postselection in the collective attack scenario. The effect of a non-ideal error correction and two-way communication in the classical post-processing step is also taken into account.

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arXiv2007

Quantum Cryptography: from Theory to Practice

Quantum cryptography can, in principle, provide unconditional security guaranteed by the law of physics only. Here, we survey the theory and practice of the subject and highlight some recent developments.

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arXiv2006

Nonlinear entanglement witnesses, covariance matrices and the geometry of separable states

Entanglement witnesses provide a standard tool for the analysis of entanglement in experiments. We investigate possible nonlinear entanglement witnesses from several perspectives. First, we demonstrate that they can be used to show that the set of separable states has no facets. Second, we give a new derivation of nonlinear witnesses based on covariance matrices. Finally, we investigate extensions to the multipartite case.

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arXiv2006

Efficiency of coherent state quantum cryptography in the presence of loss: Influence of realistic error correction

We investigate the performance of continuous variable quantum key distribution scheme in a practical setting. More specifically, we take non-ideal error reconciliation procedure into account. The quantum channel connecting the two honest parties is assumed to be lossy but noiseless. Secret key rates are given for the case that the measurement outcomes are postselected or a reverse reconciliation scheme is applied. The reverse reconciliation scheme loses its initial advantage in the practical setting. If one combines postselection with reverse reconciliation however, much of this advantage can be recovered.

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arXiv2006

Upper bound on the secret key rate distillable from effective quantum correlations with imperfect detectors

We provide a simple method to obtain an upper bound on the secret key rate that is particularly suited to analyze practical realizations of quantum key distribution protocols with imperfect devices. We consider the so-called trusted device scenario where Eve cannot modify the actual detection devices employed by Alice and Bob. The upper bound obtained is based on the available measurements results, but it includes the effect of the noise and losses present in the detectors of the legitimate users.

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arXiv2006

Simple criteria for projective measurements with linear optics

We derive a set of criteria to decide whether a given projection measurement can be, in principle, exactly implemented solely by means of linear optics. The derivation can be adapted to various detection methods, including photon counting and homodyne detection. These criteria enable one to obtain easily No-Go theorems for the exact distinguishability of orthogonal quantum states with linear optics including the use of auxiliary photons and conditional dynamics.

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arXiv2006

Implementing Non-Projective Measurements via Linear Optics: an Approach Based on Optimal Quantum State Discrimination

We discuss the problem of implementing generalized measurements (POVMs) with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an optimization problem for a chosen cost function. We formulate a general principle: the implementation is only possible if a linear-optics circuit exists for which the quantum mechanical optimum (minimum) is still attainable after dephasing the corresponding quantum states. The general principle enables us, for instance, to derive a set of necessary conditions for the linear-optics implementation of the POVM that realizes the quantum mechanically optimal unambiguous discrimination of two pure nonorthogonal states. This extends our previous results on projection measurements and the exact discrimination of orthogonal states.

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arXiv2006

Nonlinear entanglement witnesses

Entanglement detection typically relies on linear inequalities for mean values of certain observables (entanglement witnesses), where violation indicates entanglement. We provide a general method to improve any of these inequalities for bipartite systems via nonlinear expressions. The nonlinearities are of different orders and can be directly measured in experiments, often without any extra effort.

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arXiv2006

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.

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arXiv2006

Binary projective measurement via linear optics and photon counting

We investigate the implementation of binary projective measurements with linear optics. This problem can be viewed as a single-shot discrimination of two orthogonal pure quantum states. We show that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. The statement holds in the asymptotic limit of large number of these physical resources.

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arXiv2006

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.

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arXiv2005

Implementation of projective measurements with linear optics and continuous photon counting

We investigate the possibility of implementing a given projection measurement using linear optics and arbitrarily fast feedforward based on the continuous detection of photons. In particular, we systematically derive the so-called Dolinar scheme that achieves the minimum error discrimination of binary coherent states. Moreover, we show that the Dolinar-type approach can also be applied to projection measurements in the regime of photonic-qubit signals. Our results demonstrate that for implementing a projection measurement with linear optics, in principle, unit success probability may be approached even without the use of expensive entangled auxiliary states, as they are needed in all known (near-)deterministic linear-optics proposals.

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arXiv2005

Optimal Unambiguous State Discrimination of two density matrices and its link with the Fidelity

Recently the problem of Unambiguous State Discrimination (USD) of mixed quantum states has attracted much attention. So far, bounds on the optimum success probability have been derived [1]. For two mixed states they are given in terms of the fidelity. Here we give tighter bounds as well as necessary and sufficient conditions for two mixed states to reach these bounds. Moreover we construct the corresponding optimal measurement strategies. With this result, we provide analytical solutions for unambiguous discrimination of a class of generic mixed states. This goes beyond known results which are all reducible to some pure state case. Additionally, we show that examples exist where the bounds cannot be reached.

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arXiv2005

Intercept-resend attacks in the Bennett-Brassard 1984 quantum key distribution protocol with weak coherent pulses

Unconditional security proofs of the Bennett-Brassard protocol of quantum key distribution have been obtained recently. These proofs cover also practical implementations that utilize weak coherent pulses in the four signal polarizations. Proven secure rates leave open the possibility that new proofs or new public discussion protocols obtain larger rates over increased distance. In this paper we investigate limits to error rate and signal losses that can be tolerated by future protocols and proofs.

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