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We address side-channel leakage in a trusted preparation station of continuous-variable quantum key distribution with coherent and squeezed states. We consider two different scenarios: multimode Gaussian modulation, directly accessible to an eavesdropper, or side-channel loss of the signal states prior to the modulation stage. We show the negative impact of excessive modulation on both the coherent-and squeezed-state protocols. The impact is more pronounced for squeezed-state protocols and may require optimization of squeezing in the case of noisy quantum channels. Further, we demonstrate that the coherent-state protocol is immune to side-channel signal state leakage prior to modulation, while the squeezed-state protocol is vulnerable to such attacks, becoming more sensitive to the noise in the channel. In the general case of noisy quantum channels the signal squeezing can be optimized to provide best performance of the protocol in the presence of side-channel leakage prior to modulation. Our results demonstrate that leakage from the trusted source in continuous-variable quantum key distribution should not be underestimated and squeezing optimization is needed to overcome coherent state protocols.

The role of the side channels in the continuous-variable quantum key distribution is studied. It is shown how the information leakage through a side channel from the trusted sender station increases the vulnerability of the protocols to the eavesdropping in the main quantum communication channel. Moreover, the untrusted noise infusion by an eavesdropper on the trusted receiving side breaks the security even for a purely attenuating main quantum channel. As a method to compensate for the effect of the side-channel leakage on the sender side, we suggest several types of manipulations on the side-channel input. It is shown that by applying the modulated coherent light on the input of the side channel that is optimally correlated to the modulation on the main signal and optionally, introducing additional squeezing in the case of the squeezed-state protocol, the negative influence of the lossy side channel on the sender side can be completely removed. For the trusted receiving side, the method of optimal monitoring of the residual noise from the side-channel noise infusion is suggested and shown to be able to completely eliminate the presence of the noisy side channel. We therefore prove that the side-channel effects can be completely removed using feasible operations if the trusted parties access the respective parts of the side channels. PACS numbers: 03.67.Hk, 03.67.Dd I. INTRODUCTIONQuantum key distribution (QKD) [1, 2] is a major communication application of quantum information theory aiming at the development of protocols for establishing secure channels protected by the laws of quantum physics. Such channels can then be used to share a secure key for classical symmetrical cryptographic systems. Recently, continuous-variable (CV) [3] protocols of QKD (see [4] for review) were developed and implemented on the basis of squeezed [5][6][7] or coherent [8][9][10][11][12] states. The security of CV QKD protocols in the case of Gaussian modulation was then shown against collective attacks in the presence of channel noise [13,14], which also implies the security against the most general coherent attacks [15,16].CV QKD protocols, however, suffer from various imperfections. The most threatening are the untrusted (i.e., being under full control of a potential eavesdropper) quantum channels, which are inclined to losses due to the attenuation and can add excess noise in the link. Such noise can also be detection noise indistinguishable from the effect of the channel. In security analysis it is then supposed that all the channel imperfections are due to the presence on an eavesdropper. It was an important step in the development of CV QKD when with the use of reverse reconciliation it was shown possible to establish asymptotically secure key transmission upon any pure channel loss [9], while noise remains limiting to the security of the protocols.However, the insecure quantum channel is not neces- * Electronic address: ivan.derkach01@upol.cz †

Flaws in the process of modulation, or encoding of key bits in the quadratures of the electromagnetic light field, can make continuous-variable quantum key distribution systems susceptible to leakage of secret information. Here, we report such a modulation leakage vulnerability in a system that uses an optical in-phase and quadrature modulator to implement a single sideband encoding scheme. The leakage arises from the limited suppression of a quantuminformation-carrying sideband during modulation. Based on the results from a proof-of-concept experiment, we theoretically analyse the impact of this vulnerability. Our results indicate that the leakage reduces the range over which a positive secret key can be obtained, and can even lead to a security breach if not properly taken into account. We also study the effectiveness of additional trusted noise as a countermeasure to this vulnerability.

We propose the Gaussian continuous-variable quantum key distribution using squeezed states in the composite channels including atmospheric propagation with transmittance fluctuations. We show that adjustments of signal modulation and use of optimal feasible squeezing can be sufficient to significantly overcome the coherent-state protocol and drastically improve the performance of quantum key distribution in atmospheric channels, also in the presence of additional attenuating and noisy channels. Furthermore, we consider examples of atmospheric links of different lengths, and show that optimization of both squeezing and modulation is crucial for reduction of protocol downtime and increase of secure atmospheric channel distance. Our results demonstrate unexpected advantage of fragile squeezed states of light in the free-space quantum key distribution applicable in daylight and stable against atmospheric turbulence.Quantum key distribution (QKD) [1-5] is one of the major practical applications of quantum information theory, which provides trusted parties (Alice and Bob) with the methods (protocols) for provably secure distribution of secret cryptographic keys so that security of the key can be verified using fundamental principles of quantum physics. One of the main requirements of QKD is the availability of a dedicated quantum channel capable of transmitting coherent quantum signals between the sending and receiving stations. In the case of fiber-optical channels, being the typical media for QKD implementations, this means a dedicated optical fiber, possibly with co-existing classical or quantum signals. However, the dedicated fiber-optical infrastructure can be unavailable, e.g., in the case of movable stations, necessity of quick channel deployment or in hostile environments. Moreover, the extra-long-distance inter-continental quantum communication over satellites relies on the free-space channels [6]. Therefore, the free-space channels are an important physical medium for QKD implementations.The main issue faced by the discrete-variable (DV) QKD protocols, based on single-photon states or weak coherent pulses and the direct photon counting, is the sensitivity of the detectors to the background light, which adds noise to the measured data. This renders standard DV QKD protocols practically unusable in the daylight conditions unless spectral filtering is applied, which adds unwanted additional loss and complexity to the set-up. At the same time, applicability and efficiency are crucial for QKD as they directly affect the secret communication, based on the quantum-secure keys. Alternatively, continuous-variable (CV) QKD protocols [7-10], based on the multiphoton coherent [11][12][13][14][15] or squeezed states [16] and homodyne quadrature detection using off-the-shelf equipment, can overcome this limitation. Indeed, a homodyne detector, which matches a signal to a narrow-band local oscillator (LO) beam, being the phase reference for the measurement, can intrinsically filter out the background radiation and make CV Q...

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We address the applicability of quantum key distribution with continuous-variable coherent and squeezed states over long-distance satellite-based links, considering low Earth orbits and taking into account strong varying channel attenuation, atmospheric turbulence and finite data ensemble size effects. We obtain tight security bounds on the untrusted excess noise on the channel output, which suggest that substantial efforts aimed at setup stabilization and reduction of noise and loss are required, or the protocols can be realistically implemented over satellite links once either individual or passive collective attacks are assumed. Furthermore, splitting the satellite pass into discrete segments and extracting the key from each rather than from the overall single pass allows one to effectively improve robustness against the untrusted channel noise and establish a secure key under active collective attacks. We show that feasible amounts of optimized signal squeezing can substantially improve the applicability of the protocols allowing for lower system clock rates and aperture sizes and resulting in higher robustness against channel attenuation and noise compared to the coherent-state protocol.

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