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Experimentelle Kryptographie mit kontinuierlichen Variablen

Stefan Lorenz

Published Jan 1, 2005• 0 citations

Abstract

This thesis presents experimental realizations of quantum key distribution (QKD) systems which are based on continuous variables. As such, polarization or amplitude and phase of a light field are used, in contrast to discrete variables like the photon number. One QKD-system examined in this work is based on the entanglement of intense light pulses in the amplitude and phase quadratures. A measurement system for these observables is built and characterized. The existing measurement procedures can be optimized in speed, such that a observation of entanglement at a rate of 100 kHz is possible. Future improvements of the measurement system to obtain a secure key generation are presented. The second group of experimentally investigated QKD-setups uses classical coherent states and homodyne detection. An absolute correspondence between the quantum mechanical description of the system and the state preparation and measurement apparatus is given. It is shown that quadrature variables can be substituted with polarization variables, providing significant technical advantages. A setup to generate arbitrary continuous variable polarization states is built and characterized, as well as a low noise, broadband and high efficiency homodyne polarization detection system. Its overall efficiency, including optical and photodiode loss, and interference visibility is up to 88%. Using these setups, different coding schemes for quantum key generation were implemented. Transmissions with pulse rates of 100 kHz and quantum channel losses up to 74% (-5.9 dB respectively) were experimentally simulated. By using the post selection method, correlated key pairs secure against beam splitting attacks could be obtained. A special detection setup, using simultaneous measurement of conjugate polarization observables, provides tomographical data (e.g. the Q-function) of the transmitted states. Thus, an advanced security analysis against more general attacks will be possible.

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Optical homodyne detection is widely adopted in continuous-variable quantum key distribution for high-rate field measurement quadratures. Besides that, those detection schemes have been being implemented for single-photon statistics characterization in the field of quantum tomography. In this work, we propose a discrete-variable quantum key distribution (DV-QKD) implementation that combines the use of phase modulators for high-speed state of polarization (SOP) generation, with a conjugate homodyne detection scheme which enables the deployment of high speed QKD systems. The channel discretization relies on the application of a detection threshold that allows to map the measured voltages as a click or no-click. Our scheme relies also on the use of a time-multiplexed pilot tone-quantum signal architecture which enables the use of a Bob locally generated local oscillator and opens the door to an effective polarization drift compensation scheme. Besides that, our results shows that for higher detection threshold values we obtain a very low quantum bit error rate (QBER) on the sifted key. Nevertheless, due to huge number of discarded qubits the obtained secure key length abruptly decreases. From our results, we observe that optimizing the detection threshold and considering a system operating at 500 MHz symbol generation clock, a secure key rate of approximately 46.9 Mbps, with a sifted QBER of [Formula: see text] over 40 km of optical fiber. This considering the error correction and privacy amplification steps necessary to obtain a final secure key.

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arXiv:0812.3292•New Journal of Physics•Apr 30, 2009•217 citations

This thesis presents experimental realizations of quantum key distribution (QKD) systems which are based on continuous variables. As such, polarization or amplitude and phase of a light field are used, in contrast to discrete variables like the photon number. One QKD-system examined in this work is based on the entanglement of intense light pulses in the amplitude and phase quadratures. A measurement system for these observables is built and characterized. The existing measurement procedures can be optimized in speed, such that a observation of entanglement at a rate of 100 kHz is possible. Future improvements of the measurement system to obtain a secure key generation are presented. The second group of experimentally investigated QKD-setups uses classical coherent states and homodyne detection. An absolute correspondence between the quantum mechanical description of the system and the state preparation and measurement apparatus is given. It is shown that quadrature variables can be substituted with polarization variables, providing significant technical advantages. A setup to generate arbitrary continuous variable polarization states is built and characterized, as well as a low noise, broadband and high efficiency homodyne polarization detection system. Its overall efficiency, including optical and photodiode loss, and interference visibility is up to 88%. Using these setups, different coding schemes for quantum key generation were implemented. Transmissions with pulse rates of 100 kHz and quantum channel losses up to 74% (-5.9 dB respectively) were experimentally simulated. By using the post selection method, correlated key pairs secure against beam splitting attacks could be obtained. A special detection setup, using simultaneous measurement of conjugate polarization observables, provides tomographical data (e.g. the Q-function) of the transmitted states. Thus, an advanced security analysis against more general attacks will be possible.

Optical homodyne detection is widely adopted in continuous-variable quantum key distribution for high-rate field measurement quadratures. Besides that, those detection schemes have been being implemented for single-photon statistics characterization in the field of quantum tomography. In this work, we propose a discrete-variable quantum key distribution (DV-QKD) implementation that combines the use of phase modulators for high-speed state of polarization (SOP) generation, with a conjugate homodyne detection scheme which enables the deployment of high speed QKD systems. The channel discretization relies on the application of a detection threshold that allows to map the measured voltages as a click or no-click. Our scheme relies also on the use of a time-multiplexed pilot tone-quantum signal architecture which enables the use of a Bob locally generated local oscillator and opens the door to an effective polarization drift compensation scheme. Besides that, our results shows that for higher detection threshold values we obtain a very low quantum bit error rate (QBER) on the sifted key. Nevertheless, due to huge number of discarded qubits the obtained secure key length abruptly decreases. From our results, we observe that optimizing the detection threshold and considering a system operating at 500 MHz symbol generation clock, a secure key rate of approximately 46.9 Mbps, with a sifted QBER of [Formula: see text] over 40 km of optical fiber. This considering the error correction and privacy amplification steps necessary to obtain a final secure key.

We have developed a continuous-variable quantum key distribution (CV-QKD) system that employs discrete quadrature-amplitude modulation and homodyne detection of coherent states of light. We experimentally demonstrated automated secure key generation with a rate of 50 kbps when a quantum channel is a 10 km optical fibre. The CV-QKD system utilises a four-state and post-selection protocol and generates a secure key against the entangling cloner attack. We used a pulsed light source of 1550 nm wavelength with a repetition rate of 10 MHz. A commercially available balanced receiver is used to realise shot-noise-limited pulsed homodyne detection. We used a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification. A graphical processing unit card is used to accelerate the software-based post-processing.

Optical homodyne detection has been widely used in continuous-variable (CV) quantum information processing for measuring field quadrature. In this paper we explore the possibility of operating a conjugate homodyne detection system in ``photon counting'' mode to implement discrete-variable (DV) quantum key distribution (QKD). A conjugate homodyne detection system, which consists of a beam splitter followed by two optical homodyne detectors, can simultaneously measure a pair of conjugate quadratures

X

and

P

of the incoming quantum state. In classical electrodynamics,

{X}^{2}+{P}^{2}

is proportional to the energy (the photon number) of the input light. In quantum optics,

X

and

P

do not commute and thus the above photon-number measurement is intrinsically noisy. This implies that a blind application of standard security proofs of QKD could result in pessimistic performance. We overcome this obstacle by taking advantage of two special features of the proposed detection scheme. First, the fundamental detection noise associated with vacuum fluctuations cannot be manipulated by an external adversary. Second, the ability to reconstruct the photon number distribution at the receiver's end can place additional constraints on possible attacks from the adversary. As an example, we study the security of the BB84 QKD using conjugate homodyne detection and evaluate its performance through numerical simulations. This study may open the door to a family of QKD protocols, complementary to the well-established DV-QKD based on single-photon detection and CV-QKD based on coherent detection.

We report on the development of continuous-variable quantum key distribution (CV-QKD) system that are based on discrete quadrature amplitude modulation (QAM) and homodyne detection of coherent states of light. We use a pulsed light source whose wavelength is 1550 nm and repetition rate is 10 MHz. The CV-QKD system can continuously generate secret key which is secure against entangling cloner attack. Key generation rate is 50 kbps when the quantum channel is a 10 km optical fiber. The CV-QKD system we have developed utilizes the four-state and post-selection protocol [T. Hirano, et al., Phys. Rev. A 68, 042331 (2003).]; Alice randomly sends one of four states {|±α⟩,|±𝑖α⟩}, and Bob randomly performs x- or p- measurement by homodyne detection. A commercially available balanced receiver is used to realize shot-noise-limited pulsed homodyne detection. GPU cards are used to accelerate the software-based post-processing. We use a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification.

Quantum continuous variables (CV) have been explored as an alternative to qubits for quantum key distribution (QKD). More specifically, protocols using coherent states and homodyne or heterodyne measurements have been proposed and experimentally demonstrated (Grosshans et al., 2003). Relying on technologies allowing much higher rates than allowed by the single photon detectors used in qubit based QKD, those protocols are the only ones which could allow key rates in the GHz range in the foreseeable future. Furthermore, their security proofs have recently been extendend to generic attacks in the case of gaussian modulation. However, to our knowledge, all security analyses up to know have implicitely assumed Bob's measurement setup to use a homo- or heterodyne detection with an external classical phase reference, while the experimental realizations use a lightbeam for this role. This beam doesn't carry any information useful to the spy, and any attack on its phase could equally be carried on the signal beam. However, the intensity of this beam is used in experimental implementations to calibrate the quantum noise level. This calibration is then used to determine the channel gain, which is an important parameter of Eve's attack. We show that this allows Eve to implement an intercepte resend attack forbiding QKD as soon as the losses are above 3dB. We also give simple countermeasures to this new class of attacks.

We have designed and realized a prototype that implements a continuous-variable quantum key distribution (QKD) protocol based on coherent states and reverse reconciliation. The system uses time and polarization multiplexing for optimal transmission and detection of the signal and phase reference, and employs sophisticated error-correction codes for reconciliation. The security of the system is guaranteed against general coherent eavesdropping attacks. The performance of the prototype was tested over preinstalled optical fibres as part of a quantum cryptography network combining different QKD technologies. The stable and automatic operation of the prototype over 57 h yielded an average secret key distribution rate of 8 kbit s −1 over a 3 dB loss optical fibre, including the key extraction process and all quantum and classical communication. This system is therefore ideal for securing communications in metropolitan size networks with high-speed requirements.