High-dimensional measurement-device-independent quantum key distribution on two-dimensional subspaces

Abstract

Quantum key distribution (QKD) provides ultimate cryptographic security based on the laws of quantum mechanics. For point-to-point QKD protocols, the security of the generated key is compromised by detector side channel attacks. This problem can be solved with measurement device independent QKD (mdi-QKD). However, mdi-QKD has shown limited performances in terms of the secret key generation rate, due to post-selection in the Bell measurements. We show that high dimensional (Hi-D) encoding (qudits) improves the performance of current mdi-QKD implementations. The scheme is proven to be unconditionally secure even for weak coherent pulses with decoy states, while the secret key rate is derived in the single photon case. Our analysis includes phase errors, imperfect sources and dark counts to mimic real systems. Compared to the standard bidimensional case, we show an improvement in the key generation rate. * luca.delantonio@nbi.ku.dk † dabac@fotonik.dtu.dk to increase the dimension of the Hilbert space [19-23] for standard QKD. We propose a protocol, where Alice and Bob generate qudits (quantum states in N -dimensions) encoded in different paths or time slots of the photons. These photons then interfere at Charlie's Beam Splitters (BS), as shown in Fig. 1. As discussed below, the measurement projects the qubits into a two dimensional subspace, which can be used for QKD. In the following, we analyse this high dimensional mdi-QKD protocol, considering the main sources of errors, such as, imperfect photon generation, dark counts and (unknown) phase shifts. We prove that high dimensional mdi-QKD is unconditionally secure for coherent states with the decoy state technique [15,24], and analyse the key generation rate for single photon sources. In analogy to a similar result for standard QKD [23], we find that our Hi-D mdi-QKD protocol is advantageous, particularly in the detector saturation regime, where the time between photon clicks at Charlie's detectors is comparable to the detectors' dead time τ d . We study the protocol both for time and space encoding, and analyse the practical constraints that make one encoding better than the other. A different Hi-D mdi-QKD scheme was proposed in Ref. [18], but remains experimentally unfeasible, since discriminating Bell states in high dimensions is impossible by simple means [25,26]. In comparison, our protocol can be implemented without significant increase in the complexity of existing setups. In particular, for weak coherent states and time encoding, no change in the hardware is required. Protocol definitionMost QKD protocols are based on mutually unbiased bases (MUBs). Usually, the computational Z basis ({|0 , |1 } for qubits) is less susceptible to errors than arXiv:1809.04405v1 [quant-ph]

High‐Dimensional Quantum Communication: Benefits, Progress, and Future Challenges

“…Device‐independent (DI) protocols or measurement‐device‐independent protocols (MDI) can overcome these limitations . In this direction, two proof‐of‐concept of high‐dimensional QKD in an MDI scheme has been proposed and proved…”

Quantum key distribution with two-way authentication

“…According to the verification results, Alice and Bob determine what information they should keep. Due to the low generation rate of MDI protocol, high-dimensional MDI (Dellantonio et al 2018) is invented, which makes the quantum state with more information and increases the key generation rate. In fact, in quantum theory, high-dimensional quantum states can be composed of multiple two-dimensional quantum states, which is the reason why highdimensional quantum states can be converted into time-sharing two-dimensional MDI.…”

“…When the error rate is high (Khan 2009;Xu et al 2020), high-dimensional quantum states can also increase the key generation rate. Hd-MDI (Dellantonio et al 2018) is also a method to deal with high loss channels.…”

“…In this paper, we present a quantum key distribution protocol with two-way authentication. It uses some recent quantum technologies, such as QKD with pseudo-random number (Trushechkin et al 2017), multi group quantum coding bases, Measurement-deviceindependent(MDI) QKD (Lo et al 2012) and high-dimensional(HD) MDI QKD (Dellantonio et al 2018). We prove the reliability of identity authentication and the security of quantum key distribution.…”

Efficient High-Dimensional Quantum Key Distribution with Hybrid Encoding

“…It has been also found that the efficiency of key distribution increases with qudits in an ideal situation [ 32 , 33 , 34 , 35 , 36 ]. Various high-dimensional QKD protocols have been proposed such as a generalized version of BB84, a multipartite high-dimensional QKD [ 37 ], and MDI-QKDs using high-dimensional quantum states [ 38 , 39 , 40 ]. Moreover, QKD protocols using qudits have been implemented experimentally in various quantum system, for instance, energy-time eigenstates [ 41 , 42 , 43 , 44 , 45 ] and orbital angular momentum (OAM) mode of a single photon [ 46 , 47 , 48 , 49 , 50 ].…”