Abstracts
Jean-Daniel Bancal
To date, most efforts to demonstrate quantum nonlocality have concentrated on systems of single (or very few) particles. It is however difficult in many experiments (e.g. on many-body systems) to address single particles, making it hard to highlight the presence of nonlocality. We show how a natural setup with no access to individual particles allows to violate the CHSH inequality with many pairs, including in our analysis effects of noise. We discuss the case of distinguishable and indistinguishable particles. Finally, a comparison of these two situations provides new insight into the complex relation between entanglement and nonlocality.
Normand Beaudry
Squashing Models for Optical Measurements in Quantum Communication
Measurements with photodetectors necessarily need to be described in the infinite dimensional Fock space of one or several modes. For some measurements a model has been postulated which describes the full mode measurement as a composition of a mapping (squashing) of the signal into a small dimensional Hilbert space followed by a specified target measurement. We present a formalism to investigate whether a given measurement pair of mode and target measurements can be connected by a squashing model. We show that the measurements used in the BB84 protocol do allow a squashing description, although the six-state protocol does not. As a result, security proofs for the BB84 protocol can be based on the assumption that the eavesdropper forwards at most one photon, while the same does not hold for the six-state protocol.
Measurements with photodetectors necessarily need to be described in the infinite dimensional Fock space of one or several modes. For some measurements a model has been postulated which describes the full mode measurement as a composition of a mapping (squashing) of the signal into a small dimensional Hilbert space followed by a specified target measurement. We present a formalism to investigate whether a given measurement pair of mode and target measurements can be connected by a squashing model. We show that the measurements used in the BB84 protocol do allow a squashing description, although the six-state protocol does not. As a result, security proofs for the BB84 protocol can be based on the assumption that the eavesdropper forwards at most one photon, while the same does not hold for the six-state protocol.
Anne Broadbent
How to use a quantum computer without having to trust it
We consider the scenario where a classical user wishes to interface with a quantum computer in order to perform a quantum computation, but is unwilling to reveal her input, output or even the function that she is computing. We call this task "universal blind quantum computation", and show how to accomplish it with information-theoretic security.
Joint work with Joseph Fitzsimons (Oxford) and Elham Kashefi (Edinburgh)
We consider the scenario where a classical user wishes to interface with a quantum computer in order to perform a quantum computation, but is unwilling to reveal her input, output or even the function that she is computing. We call this task "universal blind quantum computation", and show how to accomplish it with information-theoretic security.
Joint work with Joseph Fitzsimons (Oxford) and Elham Kashefi (Edinburgh)
André Chailloux
Increasing the power of the verifier in Quantum Zero Knowledge.
In quantum zero knowledge, the assumption was made that the verifier is only using unitary operations. Under this assumption, many nice properties have been shown about quantum zero knowledge, including the fact that Honest-Verifier Quantum Statistical Zero Knowledge (HVQSZK) is equal to Cheating-Verifier Quantum Statistical Zero Knowledge (QSZK) (see [Wat02,Wat06]).
In this paper, we study what happens when we allow an honest verifier to flip some coins in addition to using unitary operations. Flipping a coin is a non-unitary operation but doesn't seem at first to enhance the cheating possibilities of the verifier since a classical honest verifier can flip coins. In this setting, we show an unexpected result: any classical Interactive Proof has an Honest-Verifier Quantum Statistical Zero Knowledge proof with coins. Note that in the classical case, honest verifier SZK is no more powerful than SZK and hence it is not believed to contain even NP. On the other hand, in the case of cheating verifiers, we show that Quantum Statistical Zero Knowledge where the verifier applies any non-unitary operation is equal to Quantum Zero-Knowledge where the verifier uses only unitaries.
One can think of our results in two complementary ways.
If we would like to use the honest verifier model as a means to study the general model by taking advantage of their equivalence, then it is imperative to use the unitary definition without coins, since with the general one this equivalence is most probably not true.
On the other hand, if we would like to use quantum zero knowledge protocols in a cryptographic scenario where the honest-but-curious model is sufficient, then adding the unitary constraint severely decreases the power of quantum zero knowledge protocols.
In quantum zero knowledge, the assumption was made that the verifier is only using unitary operations. Under this assumption, many nice properties have been shown about quantum zero knowledge, including the fact that Honest-Verifier Quantum Statistical Zero Knowledge (HVQSZK) is equal to Cheating-Verifier Quantum Statistical Zero Knowledge (QSZK) (see [Wat02,Wat06]).
In this paper, we study what happens when we allow an honest verifier to flip some coins in addition to using unitary operations. Flipping a coin is a non-unitary operation but doesn't seem at first to enhance the cheating possibilities of the verifier since a classical honest verifier can flip coins. In this setting, we show an unexpected result: any classical Interactive Proof has an Honest-Verifier Quantum Statistical Zero Knowledge proof with coins. Note that in the classical case, honest verifier SZK is no more powerful than SZK and hence it is not believed to contain even NP. On the other hand, in the case of cheating verifiers, we show that Quantum Statistical Zero Knowledge where the verifier applies any non-unitary operation is equal to Quantum Zero-Knowledge where the verifier uses only unitaries.
One can think of our results in two complementary ways.
If we would like to use the honest verifier model as a means to study the general model by taking advantage of their equivalence, then it is imperative to use the unitary definition without coins, since with the general one this equivalence is most probably not true.
On the other hand, if we would like to use quantum zero knowledge protocols in a cryptographic scenario where the honest-but-curious model is sufficient, then adding the unitary constraint severely decreases the power of quantum zero knowledge protocols.
Chris Erven
Entangled Quantum Key Distribution Over Two Free-Space Optical Links
Agnes Ferenczi
Symmetries in QKD Security Proofs
We address the question of optimal eavesdropping strategies in quantum key distribution (QKD) protocols.
For many QKD protocols the optimal eavesdropping attacks have been calculated. In retrospect, the optimal eavesdropping strategy was identified with an optimal cloner for many protocols (e.g BB84 protocol, six-state protocol or continuous variable QKD). In some situations, however, we fail to identify a cloner with the calculated optimal attack.
We want to find a way to predict if the optimal eavesdropping attack is indeed an optimal cloner, based on knowing the signal states and measurements of the QKD protocol and by exploiting symmetry properties of the corresponding quantum system.
We address the question of optimal eavesdropping strategies in quantum key distribution (QKD) protocols.
For many QKD protocols the optimal eavesdropping attacks have been calculated. In retrospect, the optimal eavesdropping strategy was identified with an optimal cloner for many protocols (e.g BB84 protocol, six-state protocol or continuous variable QKD). In some situations, however, we fail to identify a cloner with the calculated optimal attack.
We want to find a way to predict if the optimal eavesdropping attack is indeed an optimal cloner, based on knowing the signal states and measurements of the QKD protocol and by exploiting symmetry properties of the corresponding quantum system.
Manuel Forster
The Universality of Non-Local Boxes
One of the most fascinating consequences of quantum theory is non-locality, i.e., the fact
that the behavior under measurements of (spatially separated) parts of a system can have a correlation unexplainable by shared classical information. At the same time, these correlations are no-signaling and do not allow for message transmission. Popescu and Rohrlich have defined a non-local box as a ''basic building block of non-locality'' and initiated a systematic study of non-local correlations and their applications. They left open, however, whether any no-signaling correlation can be simulated by such non-local boxes. We show that the answer is yes with respect to arbitrarily accurate approximations.
One of the most fascinating consequences of quantum theory is non-locality, i.e., the fact
that the behavior under measurements of (spatially separated) parts of a system can have a correlation unexplainable by shared classical information. At the same time, these correlations are no-signaling and do not allow for message transmission. Popescu and Rohrlich have defined a non-local box as a ''basic building block of non-locality'' and initiated a systematic study of non-local correlations and their applications. They left open, however, whether any no-signaling correlation can be simulated by such non-local boxes. We show that the answer is yes with respect to arbitrarily accurate approximations.
Esther Haenggi
How Non-Local are n Noisy Popescu-Rohrlich Machines?
It is a well-known feature of Quantum Mechanics that its measurement statistics can be non-local, i.e., they cannot be explained with pre-shared randomness. Quantum Mechanics is non-local but not maximally so. For example, it can only approximate a Popescu-Rohrlich Machine by roughly 85%. We study the question of how much non-locality there is in (a number of) imperfect Popescu-Rohrlich Machines. Our main result is that the local part of n Popescu-Rohrlich Machines with error epsilon is of order epsilon^{ceiling{n/2}}.
It is a well-known feature of Quantum Mechanics that its measurement statistics can be non-local, i.e., they cannot be explained with pre-shared randomness. Quantum Mechanics is non-local but not maximally so. For example, it can only approximate a Popescu-Rohrlich Machine by roughly 85%. We study the question of how much non-locality there is in (a number of) imperfect Popescu-Rohrlich Machines. Our main result is that the local part of n Popescu-Rohrlich Machines with error epsilon is of order epsilon^{ceiling{n/2}}.
Jim Harrington
When properly implemented, quantum key distribution protocols offer unconditional security in the asymptotic limit for two parties to share secret bits. In the finite case, privacy can still be achieved with high confidence, although the secret bit yield may differ dramatically from the asymptotic case.
It is thus important to rigorously develop security statements for finite-length keys, as well as to account for imperfections in realistic devices. In this poster, we will present the approach we have been following at Los Alamos National Laboratory, which incorporates important results from Koashi and Renner.
It is thus important to rigorously develop security statements for finite-length keys, as well as to account for imperfections in realistic devices. In this poster, we will present the approach we have been following at Los Alamos National Laboratory, which incorporates important results from Koashi and Renner.
Bettina Heim
Free Space Quantum Key Distribution with Coherent Polarization Variables
In our free space Quantum Key Distribution (QKD) setup we encode the signal in coherent states which allow for convenient and fast state preparation and measurement.
We utilize a pair of conjugate polarization variables (Stokes operators) as signal carriers. This offers an excellent interference between signal and local oscillator without the need for additional stabilization, as signal and local oscillator travel in the same spatial mode.
After the successful demonstration of this QKD scheme in the laboratory [1], we now present a working proof-of-principle experiment under real free space conditions: The quantum states are transmitted over 100 m on the roof of our institut's building. The use of a retro-reflector enables us to place Alice's and Bob's station on the same optical table.
Future plans are the experimental verification of effective entanglement for this setup as in [1] as well as the detailed channel characterization including beam jitter effects and transmission statistics.
And in the long term, we plan to establish a point-to-point QKD link between two distinct buildings 1.5 km apart.
[1] S. Lorenz et al., Phys. Rev. A 74, 042326 (2006).
In our free space Quantum Key Distribution (QKD) setup we encode the signal in coherent states which allow for convenient and fast state preparation and measurement.
We utilize a pair of conjugate polarization variables (Stokes operators) as signal carriers. This offers an excellent interference between signal and local oscillator without the need for additional stabilization, as signal and local oscillator travel in the same spatial mode.
After the successful demonstration of this QKD scheme in the laboratory [1], we now present a working proof-of-principle experiment under real free space conditions: The quantum states are transmitted over 100 m on the roof of our institut's building. The use of a retro-reflector enables us to place Alice's and Bob's station on the same optical table.
Future plans are the experimental verification of effective entanglement for this setup as in [1] as well as the detailed channel characterization including beam jitter effects and transmission statistics.
And in the long term, we plan to establish a point-to-point QKD link between two distinct buildings 1.5 km apart.
[1] S. Lorenz et al., Phys. Rev. A 74, 042326 (2006).
Lars Lydersen
Title: Security of quantum key distribution with bit and basis dependent detector flaws
We consider the security of the Bennett-Brassard 1984 (BB84) protocol for Quantum Key Distribution (QKD), in the presence of bit and basis dependent detector flaws. We suggest a powerful attack that can be used in systems with detector efficiency mismatch, even if the detector assignments are chosen randomly by Bob. A security proof is provided, valid for any basis dependent, linear optical imperfections in the receiver/detectors.
We consider the security of the Bennett-Brassard 1984 (BB84) protocol for Quantum Key Distribution (QKD), in the presence of bit and basis dependent detector flaws. We suggest a powerful attack that can be used in systems with detector efficiency mismatch, even if the detector assignments are chosen randomly by Bob. A security proof is provided, valid for any basis dependent, linear optical imperfections in the receiver/detectors.
Abdul Rahim Mirza
The critical nature of secure communication in our society has prompted research beyond the conventional two-node QKD setup. Quantum networks facilitate QKD ‘on-demand’ between two arbitrary network users. They consist of a number of hybrid quantum channels integrated to form a complete network. This is essential for the optimization of network throughput as some quantum channels are better suited to particular terrains. There is also greater robustness against Denial of Service attacks due to redundant lightpaths within a network. This also assists in the reduction of key relation knowledge by any adversary. A vast number of topologies are currently being envisaged, many based on present day network topologies. This will allow for transparent integration of QKD solutions into current networks.
As a subsequent development to the Durban - SmartCity project, the eThekwini Municipality funded the Quantum Research Group (QRG) to development of the first municipal quantum network in the world. The network will initially consist of a 3-4 node setup to form the backbone infrastructure linking the municipal switching offices to internal and other commercial customers. Two network architectures have been researched as part of the Quantum City project. Both the proposed networks will be implemented as trusted architectures.
The implementation of this network is intended to be realised during the third quarter of 2008. The intention is to create a basic setup and expand the network in the future to offer its services to other interested parties in the corporate sector.
After the implementation of the quantum network and general encryption of the network traffic other pronounced applications will be investigated. The enhancement of QKD through networking techniques will also be pursued.
As a subsequent development to the Durban - SmartCity project, the eThekwini Municipality funded the Quantum Research Group (QRG) to development of the first municipal quantum network in the world. The network will initially consist of a 3-4 node setup to form the backbone infrastructure linking the municipal switching offices to internal and other commercial customers. Two network architectures have been researched as part of the Quantum City project. Both the proposed networks will be implemented as trusted architectures.
The implementation of this network is intended to be realised during the third quarter of 2008. The intention is to create a basic setup and expand the network in the future to offer its services to other interested parties in the corporate sector.
After the implementation of the quantum network and general encryption of the network traffic other pronounced applications will be investigated. The enhancement of QKD through networking techniques will also be pursued.
Mohsen Razavi
DLCZ Quantum Repeaters: Rate and Fidelity Analysis
The fidelity and the rate of entanglement generation for the entanglement-swapping protocol proposed by Duan, Lukin, Cirac, and Zoller (DLCZ) [Nature 414, 413] are evaluated. We find the distance beyond which DLCZ repeaters outperform single DLCZ links by accounting for loss, multiple-excitation, and self-purification effects.
The fidelity and the rate of entanglement generation for the entanglement-swapping protocol proposed by Duan, Lukin, Cirac, and Zoller (DLCZ) [Nature 414, 413] are evaluated. We find the distance beyond which DLCZ repeaters outperform single DLCZ links by accounting for loss, multiple-excitation, and self-purification effects.
Nino Walenta
Sensitive and efficient single photon detectors are increasingly demanded e.g. for quantum key distribution (QKD) or quantum random number generation. One relatively new approach for low light detection are superconducting single photon detectors (SSPDs) which promise potentially high detection efficiency and high count rates, low dark count noise, low timing jitter and the potential for photon number resolving detection. Normally, these detectors are cooled in liquid Helium. As a step towards their practical application we have implemented such devices in a closed cycle cryostat system and used them for long distance QKD.