Performance analysis of d -dimensional quantum cryptography under state-dependent diffraction

Abstract

Standard protocols for quantum key distribution (QKD) require that the sender be able to transmit in two or more mutually unbiased bases. Here, we analyze the extent to which the performance of QKD is degraded by diffraction effects that become relevant for long propagation distances and limited sizes of apertures. In such a scenario, different states experience different amounts of diffraction, leading to state-dependent loss and phase acquisition, causing an increased error rate and security loophole at the receiver. To solve this problem, we propose a pre-compensation protocol based on pre-shaping the transverse structure of quantum states. We demonstrate, both theoretically and experimentally, that when performing QKD over a link with known, symbol-dependent loss and phase shift, the performance of QKD will be better if we intentionally increase the loss of certain symbols to make the loss and phase shift of all states same. Our results show that the pre-compensated protocol can significantly reduce the error rate induced by state-dependent diffraction and thereby improve the secure key rate of QKD systems without sacrificing the security.

Performance of real-time adaptive optics compensation in a turbulent channel with high-dimensional spatial-mode encoding

“…To solve this, one may need to introduce new protocols to mitigate mode-dependent diffraction, for example as discussed in Ref. [35].…”

“…Since the information is carried by the phase profile, OAM states are vulnerable to atmospheric turbulence. Even though the performance of OAM states in a turbulent channel has been studied both theoretically and experimentally [10,[28][29][30][31][32][33][34][35][36][37][38], realizing high-dimensional OAM-based QKD still remains challenging.To reduce the crosstalk induced by turbulence, most works either rely on post-selection of data or increasing the mode spacing (i.e. not using successive states for encoding) [10,20,33].…”

Using all transverse degrees of freedom in quantum communications based on a generic mode sorter

“…The intensity pattern of the transmitted beam can remain recognizable after a 1.6 km free-space link, and thus adaptive optics can be potentially used to mitigate turbulence [3], which can be subject to future study. In a realistic free-space link, in addition to the spatial distortion induced by turbulence which can be corrected by adaptive optics, different LG modes accumulate different amount of Gouy phase which can affect the sorting of superposition modes [10]. The Gouy phase for a LG mode can be written as φ = (2p + | | + 1) arctan(z/z R ), where z R is the Rayleigh range and z is the propagation distance.…”

“…The Gouy phase for a LG mode can be written as φ = (2p + | | + 1) arctan(z/z R ), where z R is the Rayleigh range and z is the propagation distance. As proposed in [10], pre-compensation can be used in mode preparation at the transmitter's side to guarantee that the mode-dependent phase is cancelled at the receiver's side. Furthermore, the phase-dependent phase can also be removed at the receiver's side.…”

“…Within the past few decades the orbital angular momentum (OAM) modes have received extensive attention [1][2][3][4][5] and are widely applied in various information technologies, including quantum teleportation [6], optical communications [7], and quantum key distribution [8][9][10]. Compared to the intrinsically bounded polarization state space, the OAM modes offer an infinite-dimensional Hilbert space for information encoding and therefore can be used to increase the transmission rate of a communication link.…”