Bettina Heim

Feasibility of free space quantum key distribution with coherent polarization states

Free space QKD over an atmospheric channel was demonstrated in 1996 for the first time [1]. Since then, several prepare-and-measure and entanglement-based schemes have been implemented (for a detailed overview, see [2]). All of these systems use single-photon detectors, and therefore have to employ spatial, spectral and/or temporal filtering in order to reduce background light. In our system, we use an alternative approach: with the help of a bright local oscillator (LO), we perform homodyne measurements on weak coherent polarization states [3].

Atmospheric continuous-variable quantum communication

We present a quantum communication experiment conducted over a point-to-point free-space link of 1.6 km in urban conditions. We study atmospheric influences on the capability of the link to act as a continuous-variable (CV) quantum channel. Continuous polarization states (that contain the signal encoding as well as a local oscillator (LO) in the same spatial mode) are prepared and sent over the link in a polarization multiplexed setting. Both signal and LO undergo the same atmospheric fluctuations. These are intrinsically auto-compensated which removes detrimental influences on the interferometric visibility. At the receiver, we measure the Q-function and interpret the data using the framework of effective entanglement (EE). We compare different state amplitudes and alphabets (two-state and four-state) and determine their optimal working points with respect to the distributed EE. Based on the high entanglement transmission rates achieved, our system indicates the high potential of atmospheric links in the field of CV quantum key distribution.

Studying free-space transmission statistics and improving free-space quantum key distribution in the turbulent atmosphere

The statistical fluctuations in free-space links in the turbulent atmosphere are important for the distribution of quantum signals. To that end, we first study statistics generated by the turbulent atmosphere in an entanglement- based free-space quantum key distribution (QKD) system. Using the insights gained from this analysis, we study the effect of link fluctuations on the security and key generation rate of decoy state QKD concluding that it has minimal effect in the typical operating regimes. We then investigate the novel idea of using these turbulent fluctuations to our advantage in QKD experiments. We implement a signal-to-noise ratio filter (SNRF) in our QKD system which rejects

Entanglement of Gaussian states and the applicability to quantum key distribution over fading channels

Entanglement properties of Gaussian states of light as well as the security of continuous variable quantum key distribution with Gaussian states in free-space fading channels are studied. These qualities are shown to be sensitive to the statistical properties of the transmittance distribution in the cases when entanglement is strong or when channel excess noise is present. Fading, i.e. transmission fluctuations, caused by beam wandering due to atmospheric turbulence, is a frequent challenge in free-space communication. We introduce a method of fading discrimination and subsequent post-selection of the corresponding sub-states and show that it can improve the entanglement resource and restore the security of the key distribution over a realistic fading link. Furthermore, the optimal post-selection strategy in combination with an optimized entangled resource is shown to drastically increase the protocols robustness to excess noise, which is confirmed for experimentally measured fading channel characteristics. The stability of the result against finite data ensemble size and imperfect channel estimation is also addressed.

Depolarized guided acoustic wave Brillouin scattering in hollow-core photonic crystal fibers

By performing quantum-noise-limited optical heterodyne detection, we observe polarization noise in light after propagation through a hollow-core photonic crystal fiber (PCF). We compare the noise spectrum to the one of a standard fiber and find an increase of noise even though the light is mainly transmitted in air in a hollow-core PCF. Combined with our simulation of the acoustic vibrational modes in the hollow-core PCF, we are offering an explanation for the polarization noise with a variation of guided acoustic wave Brillouin scattering (GAWBS). Here, instead of modulating the strain in the fiber core as in a solid core fiber, the acoustic vibrations in hollow-core PCF influence the effective refractive index by modulating the geometry of the photonic crystal structure. This induces polarization noise in the light guided by the photonic crystal structure.

Free space quantum key distribution with coherent polarization states

Free space QKD over an atmospheric channel was demonstrated in 1996 for the first time [1]. Since then, several prepare-and-measure and entanglement-based schemes have been implemented (for a detailed overview, see [2]). All of these systems use single-photon detectors, and therefore have to employ spatial, spectral and/or temporal filtering in order to reduce background light. In our system, we use an alternative approach: with the help of a bright local oscillator (LO), we perform homodyne measurements on weak coherent polarization states [3].

Improving entangled free-space quantum key distribution in the turbulent atmosphere

By now, free-space quantum key distribution (QKD) has seen many experiments validate the possibility of its implementation in various real world scenarios[1–4]. Recently, particular interest has focused on entanglement based QKD systems since they can tolerate higher channel losses than systems based on weak coherent laser pulses. However, while free-space channels offer tantalizing opportunities for QKD, such as using low earth orbit satellites for worldwide secure communication, only very recently has work by Semenov and Vogel [5,6] provided a theoretical foundation for the study of the transmission statistics and characteristics of free-space communication channels. In this submission, we study the influence of the turbulent atmosphere on entangled photon pairs where one photon from each pair is sent over a 1.3km free-space link. Using the system detailed in [3], with the recent update of a bright Sagnac interferometric entangled photon source[7], we study the effects of the turbulent atmosphere on the entangled properties of the photon pairs and the performance of the system using different pump rates and under various loss conditions. Already, we have been able to verify the theoretical prediction of Semenov and Vogel [5,6] that the transmission probability tends toward a log-normal distribution in highly turbulent and lossy experimental conditions as shown in Fig. 1.

Free Space Quantum Communication using Continuous Polarization Variables

We experimentally investigate atmospheric influences on quantum communication with continuous polarization variables. Signal and local oscillator are combined in one spatial mode, which leads to perfect interference at the homodyne detection. Fluctuations are thus auto-compensated.

Proof-of-principle test of coherent-state continuous variable quantum key distribution through turbulent atmosphere (Conference Presentation)

Continuous-variable quantum key distribution is a practical application of quantum information theory that is aimed at generation of secret cryptographic key between two remote trusted parties and that uses multi-photon quantum states as carriers of key bits. Remote parties share the secret key via a quantum channel, that presumably is under control of of an eavesdropper, and which properties must be taken into account in the security analysis. Well-studied fiber-optical quantum channels commonly possess stable transmittance and low noise levels, while free-space channels represent a simpler, less demanding and more flexible alternative, but suffer from atmospheric effects such as turbulence that in particular causes a non-uniform transmittance distribution referred to as fading. Nonetheless free-space channels, providing an unobstructed line-of-sight, are more apt for short, mid-range and potentially long-range (using satellites) communication and will play an important role in the future development and implementation of QKD networks. It was previously theoretically shown that coherent-state CV QKD should be in principle possible to implement over a free-space fading channel, but strong transmittance fluctuations result in the significant modulation-dependent channel excess noise. In this regime the post-selection of highly transmitting sub-channels may be needed, which can even restore the security of the protocol in the strongly turbulent channels. We now report the first proof-of-principle experimental test of coherent state CV QKD protocol using different levels Gaussian modulation over a mid-range (1.6-kilometer long) free-space atmospheric quantum channel. The transmittance of the link was characterized using intensity measurements for the reference but channel estimation using the modulated coherent states was also studied. We consider security against Gaussian collective attacks, that were shown to be optimal against CV QKD protocols . We assumed a general entangling cloner collective attack (modeled using data obtained from the state measurement results on both trusted sides of the protocol), that allows to purify the noise added in the quantum channel . Our security analysis of coherent-state protocol also took into account the effect of imperfect channel estimation, limited post-processing efficiency and finite data ensemble size on the performance of the protocol. In this regime we observe the positive key rate even without the need of applying post-selection. We show the positive improvement of the key rate with increase of the modulation variance, still remaining low enough to tolerate the transmittance fluctuations. The obtained results show that coherent-state CV QKD protocol that uses real free-space atmospheric channel can withstand negative influence of transmittance fluctuations, limited post-processing efficiency, imperfect channel estimation and other finite-size effects, and be successfully implemented. Our result paves the way to the full-scale implementation of the CV QKD in real free-space channels at mid-range distances.

Polarization noise induced by photon-phonon interaction in hollow-core photonic crystal fibres

Guided acoustic wave Brillouin scattering (GAWBS), a weak forward scattering that stems from the interaction of light with thermally excited transverse phonons, has been studied in both standard fibres [1] and photonic crystal fibres [2, 3]. The acoustic phonon vibrations modulate the stress distribution in the silica fibre core, thus modulating the refractive index and inducing polarization and phase noise in the light field.