Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding

Abstract

Conventional quantum key distribution (QKD) typically uses binary encoding based on photon polarization or time-bin degrees of freedom and achieves a key capacity of at most one bit per photon. Under photon-starved conditions the rate of detection events is much lower than the photon generation rate, because of losses in long distance propagation and the relatively long recovery times of available singlephoton detectors. Multi-bit encoding in the photon arrival times can be beneficial in such photonstarved situations. Recent security proofs indicate high-dimensional encoding in the photon arrival times is robust and can be implemented to yield high secure throughput. In this work we demonstrate entanglement-based QKD with high-dimensional encoding whose security against collective Gaussian attacks is provided by a high-visibility Franson interferometer. We achieve unprecedented key capacity and throughput for an entanglement-based QKD system because of four principal factors: Franson interferometry that does not degrade with loss; error correction coding that can tolerate high error rates; optimized time-energy entanglement generation; and highly efficient WSi superconducting nanowire single-photon detectors. The secure key capacity yields as much as 8.7 bits per coincidence. When optimized for throughput we observe a secure key rate of 2.7 Mbit s −1 after 20 km fiber transmission with a key capacity of 6.9 bits per photon coincidence. Our results demonstrate a viable approach to high-rate QKD using practical photonic entanglement and single-photon detection technologies.

50-GHz-spaced comb of high-dimensional frequency-bin entangled photons from an on-chip silicon nitride microresonator

“…We note that the original form of the 3-dimensional Bell inequality consists of 24 total measurement probabilities [36]; the reduction to 8 terms [Eq. (8)], however, is valid under the assumption of an unbiased 3 × 3 splitter and an input quantum state containing sufficient symmetries. In particular, as we show below, the above reduction holds for a density matrixρ taken to be the incoherent mixture of a maximally entangled state and white noise [37].…”

Quantifying Photonic High-Dimensional Entanglement

“…Others discussed the certification of high-dimensional entanglement using mutually unbiased basis [25,26], two-dimensional subspaces [27], or assuming that certain quantities (e.g., total angular momentum) are conserved [15]. Finally, experimental prospects for applications in quantum communications were also explored [28,29].…”

Breaking the Unbreakable: Exploiting Loopholes in Bell’s Theorem to Hack Quantum Cryptography

“…The first evidence can be found in 1999 when the effect of postselection on the Bell-CHSH inequality in the Franson interferometer was studied by Aerts et al [138]. Still, the same security test has been used in numerous experiments ever since [41][42][43][44][45][46][47][48][49][50]. We consider the lack of security in the standard Franson interferometric setup to be proven beyond doubt, but it is obvious we still have ways to go in educating the scientific community on this issue.…”

“…Since Franson's publication in 1989, the device has been experimentally tested by 6. Energy-Time Entanglement several groups [41][42][43][44][45][46][47][48][49][50], and it is often assumed to be a workable proposal for QKD. Again, we stress that the Franson scheme requires a postselection step.…”