84 research outputs found
Device-independent secret-key-rate analysis for quantum repeaters
The device-independent approach to quantum key distribution (QKD) aims to
establish a secret key between two or more parties with untrusted devices,
potentially under full control of a quantum adversary. The performance of a QKD
protocol can be quantified by the secret key rate, which can be lower bounded
via the violation of an appropriate Bell inequality in a setup with untrusted
devices. We study secret key rates in the device-independent scenario for
different quantum repeater setups and compare them to their device-dependent
analogon. The quantum repeater setups under consideration are the original
protocol by Briegel et al. and the hybrid quantum repeater protocol by van
Loock et al.. For a given repeater scheme and a given QKD protocol, the secret
key rate depends on a variety of parameters, such as the gate quality or the
detector efficiency. We systematically analyze the impact of these parameters
and suggest optimized strategies.Comment: 15 pages, 12 figure
On Global Effects Caused by Locally Noneffective Unitary Operations
Given a bipartite quantum state rho with subsystems A and B of arbitrary
dimensions, we study the entanglement detecting capabilities of locally
noneffective, or cyclic, unitary operations [L. B. Fu, Europhys. Lett., vol.
75, pp. 1-7, 2006]. Local cyclic unitaries have the special property that they
leave their target subsystem invariant. We investigate the distance between rho
and the global state after local application of such unitaries as a possible
indicator of entanglement. To this end, we derive and discuss closed formulae
for the maximal such distance achievable for three cases of interest:
(pseudo)pure quantum states, Werner states, and two-qubit states. What makes
this criterion interesting, as we show here, is that it surprisingly displays
behavior similar to recent anomalies observed for non-locality measures in
higher dimensions, as well as demonstrates an equivalence to the CHSH
inequality for certain classes of two-qubit states. Yet, despite these
similarities, the criterion is not itself a non-locality measure. We also
consider entanglement detection in bound entangled states.Comment: 16 pages, 3 figure
Limits for entanglement distribution with separable states
Entanglement distribution with separable states has recently attracted
considerable attention. Recent results suggest that quantum discord - a measure
for quantum correlations beyond entanglement - is responsible for this
counterintuitive phenomenon. In this work we study this question from a
different perspective, and find minimal requirements for a separable state to
be useful for entanglement distribution. Surprisingly, we find that the
presence of quantum discord is not sufficient to ensure entanglement
distribution: there exist states with nonzero quantum discord which
nevertheless cannot be used for entanglement distribution. As a result, we show
that entanglement distribution is not possible with rank two separable states.
Our work sheds new light on the task of entanglement distribution with
separable states, and reveals a new classification of quantum states with
respect to their usefulness for this task.Comment: 5 pages, 3 figure
Measurement-device-independent quantum key distribution with quantum memories
We generalize measurement-device-independent quantum key distribution [ H.-K.
Lo, M. Curty, and B. Qi, Phys. Rev. Lett. 108, 130503 (2012) ] to the scenario
where the Bell-state measurement station contains also heralded quantum
memories. We find analytical formulas, in terms of device imperfections, for
all quantities entering in the secret key rates, i.e., the quantum bit error
rate and the repeater rate. We assume either single-photon sources or weak
coherent pulse sources plus decoy states. We show that it is possible to
significantly outperform the original proposal, even in presence of decoherence
of the quantum memory. Our protocol may represent the first natural step for
implementing a two-segment quantum repeater
Large-scale quantum networks based on graphs
Society relies and depends increasingly on information exchange and
communication. In the quantum world, security and privacy is a built-in feature
for information processing. The essential ingredient for exploiting these
quantum advantages is the resource of entanglement, which can be shared between
two or more parties. The distribution of entanglement over large distances
constitutes a key challenge for current research and development. Due to losses
of the transmitted quantum particles, which typically scale exponentially with
the distance, intermediate quantum repeater stations are needed. Here we show
how to generalise the quantum repeater concept to the multipartite case, by
fully describing large-scale quantum networks, i.e. network nodes and their
long-distance links, in the language of graphs and graph states. This unifying
approach comprises both the distribution of multipartite entanglement across
the network, and the protection against errors via encoding. The correspondence
to graph states also provides a tool for optimising the architecture of quantum
networks.Comment: 11 pages, 5 figures, 2 tables, revised text and new results regarding
the optimisation of quantum network
Measurement-device-independent randomness generation with arbitrary quantum states
Measurements of quantum systems can be used to generate classical data that
is truly unpredictable for every observer. However, this true randomness needs
to be discriminated from randomness due to ignorance or lack of control of the
devices. We analyze the randomness gain of a measurement-device-independent
setup, consisting of a well-characterized source of quantum states and a
completely uncharacterized and untrusted detector. Our framework generalizes
previous schemes as arbitrary input states and arbitrary measurements can be
analyzed. Our method is used to suggest simple and realistic implementations
that yield high randomness generation rates of more than one random bit per
qubit for detectors of sufficient quality.Comment: 9 pages, 7 figure
Finite-range multiplexing enhances quantum key distribution via quantum repeaters
Quantum repeaters represent one possible way to achieve long-distance quantum
key distribution. Collins et al. in [Phys. Rev. Lett. 98, 060502 (2007)]
proposed multiplexing as method to increase the repeater rate and to decrease
the requirement in memory coherence time. Motivated by the experimental fact
that long-range connections are practically demanding, in this paper we extend
the original quantum repeater multiplexing protocol to the case of short-range
connection. We derive analytical formulas for the repeater rate and we show
that for short connection lengths it is possible to have most of the benefits
of a full-range multiplexing protocol. Then we incorporate decoherence of
quantum memories and we study the optimal matching for the Bell-state
measurement protocol permitting to minimize memory requirements. Finally, we
calculate the secret key rate and we show that the improvement via finite-range
multiplexing is of the same order of magnitude as via full-range multiplexing
A quantum mechanical bound for CHSH-type Bell inequalities
Many typical Bell experiments can be described as follows. A source
repeatedly distributes particles among two spacelike separated observers. Each
of them makes a measurement, using an observable randomly chosen out of several
possible ones, leading to one of two possible outcomes. After collecting a
sufficient amount of data one calculates the value of a so-called Bell
expression. An important question in this context is whether the result is
compatible with bounds based on the assumptions of locality, realism and
freedom of choice. Here we are interested in bounds on the obtained value
derived from quantum theory, so-called Tsirelson bounds. We describe a simple
Tsirelson bound, which is based on a singular value decomposition. This
mathematical result leads to some physical insights. In particular the optimal
observables can be obtained. Furthermore statements about the dimension of the
underlying Hilbert space are possible. Finally, Bell inequalities can be
modified to match rotated measurement settings, e.g. if the two parties do not
share a common reference frame.Comment: 17 pages, 7 figures, submitted for the conference proceedings of
"Quantum [Un]Speakables II: 50 Years of Bell's Theorem" in Vienna, 201
Detecting Entanglement of Unknown Quantum States with Random Measurements
In quantum information theory, the reliable and effective detection of
entanglement is of paramount importance. However, given an unknown state,
assessing its entanglement is a challenging task. To attack this problem, we
investigate the use of random local measurements, from which entanglement
witnesses are then constructed via semidefinite programming methods. We propose
a scheme of successively increasing the number of measurements until the
presence of entanglement can be unambiguously concluded, and investigate its
performance in various examples.Comment: 7 pages, 4 figures, 1 table; v2: added a reference; v3: replaced with
published versio
Secret key rates for an encoded quantum repeater
We investigate secret key rates for the quantum repeater using encoding [L.
Jiang et al., Phys. Rev. A 79, 032325 (2009)] and compare them to the standard
repeater scheme by Briegel, D\"ur, Cirac, and Zoller. The former scheme has the
advantage of a minimal consumption of classical communication. We analyze the
trade-off in the secret key rate between the communication time and the
required resources. For this purpose, we introduce an error model for the
repeater using encoding which allows for input Bell states with a fidelity
smaller than one, in contrast to the model given in [L. Jiang et al., Phys.
Rev. A 79, 032325 (2009)]. We show that one can correct additional errors in
the encoded connection procedure of this repeater and develop a suitable
decoding algorithm. Furthermore, we derive the rate of producing entangled
pairs for the quantum repeater using encoding and give the minimal parameters
(gate quality and initial fidelity) for establishing a nonzero secret key. We
find that the generic quantum repeater is optimal regarding the secret key rate
per memory per second and show that the encoded quantum repeater using the
simple three-qubit repetition code can even have an advantage with respect to
the resources compared to other recent quantum repeater schemes with encoding
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