Nurul T. Islam

Provably secure and high-rate quantum key distribution with time-bin qudits

Information encoded in high-dimensional quantum states can achieve ultrahigh rates over metropolitan distances. The security of conventional cryptography systems is threatened in the forthcoming era of quantum computers. Quantum key distribution (QKD) features fundamentally proven security and offers a promising option for quantum-proof cryptography solution. Although prototype QKD systems over optical fiber have been demonstrated over the years, the key generation rates remain several orders of magnitude lower than current classical communication systems. In an effort toward a commercially viable QKD system with improved key generation rates, we developed a discrete-variable QKD system based on time-bin quantum photonic states that can generate provably secure cryptographic keys at megabit-per-second rates over metropolitan distances. We use high-dimensional quantum states that transmit more than one secret bit per received photon, alleviating detector saturation effects in the superconducting nanowire single-photon detectors used in our system that feature very high detection efficiency (of more than 70%) and low timing jitter (of less than 40 ps). Our system is constructed using commercial off-the-shelf components, and the adopted protocol can be readily extended to free-space quantum channels. The security analysis adopted to distill the keys ensures that the demonstrated protocol is robust against coherent attacks, finite-size effects, and a broad class of experimental imperfections identified in our system.

Robust and Stable Delay Interferometers with Application to d -Dimensional Time-Frequency Quantum Key Distribution

We investigate experimentally a cascade of temperature-compensated unequal-path interferometers that can be used to measure frequency states in a high-dimensional quantum distribution system. In particular, we demonstrate that commercially-available interferometers have sufficient environmental isolation so that they maintain an interference visibility greater than 98.5\% at a wavelength of 1550 nm over extended periods with only moderate passive control of the interferometer temperature (

Reconfigurable generation and measurement of mutually unbiased bases for time-bin qudits

99\%

Building Blocks of Quantum Key Distribution

over an hour, which is mainly limited by our ability to precisely generate these states. Overall, our results indicate that these interferometers are well suited for realistic time-frequency quantum distribution protocols.

Scalable High-Dimensional Time-Bin QKD

We propose a method for implementing mutually unbiased generation and measurement of time-bin qudits using a cascade of electro-optic phase modulator–coded fiber Bragg grating pairs. Our approach requires only a single spatial mode and can switch rapidly between basis choices. We obtain explicit solutions for dimensions d = 2, 3, and 4 that realize all d + 1 possible mutually unbiased bases and analyze the performance of our approach in quantum key distribution. Given its practicality and compatibility with current technology, our approach provides a promising springboard for scalable processing of high-dimensional time-bin states.

Conclusions and Future Experiments

The first QKD scheme proposed by Bennett and Brassard in 1984 was a qubit-based (d = 2) protocol that encodes information using a photon’s polarization modes in two non-orthogonal bases (Bennett and Brassard, 1984 international conference on computers, systems & signal processing, pp 175–179, 1984; Bennett and Brassard, ACM Sigact News 20:78, 1989). Polarization is one of the many different degrees of freedom that can be used to encode information in a QKD system. The information can also be encoded using time-phase (Townsend et al., Electron Lett 29:1291, 1993; Townsend, Electron Lett 30:809, 1994; Townsend, Nature 385:47, 1997), orbital angular momentum (Spedalieri, Opt Commun 260:340 2006), etc. degrees of freedom. In this chapter, as an introductory discussion and motivation for high dimensional QKD, I describe an ideal d = 2 time-phase QKD system.

Multi-photon detection using a conventional superconducting nanowire single-photon detector

The QKD system demonstrated in Chap. 3 is based on a four-dimensional time-phase encoding scheme in which time basis states are used to generate a secret key and phase basis states are used to monitor the presence of an eavesdropper. The system can generate a secret key at a high rate, mainly due to the greater information content of the high-dimensional quantum states and a multiplexed detection scheme. Given the success of the d = 4 protocol, an important subsequent question to address is: does increasing the dimension beyond d = 4 increase the secret key rate under realistic experimental conditions?

Enhancing the secure key rate in a quantum-key-distribution system using discrete-variable, high-dimensional, time-frequency states

In this thesis, I describe and experimentally demonstrate various QKD protocols based on time-bin qudits that can generate a secret key at high rates, mainly relying on the greater information content of high-dimensional quantum photonic states and multiplexed single-photon detection schemes.

Securing quantum key distribution systems using fewer states

We present the first evidence of multi-photon detection using a conventional superconducting nanowire single-photon detector, indicating number resolution up to four photons. The observed multi-photon detection statistics are consistent with the predictions of our model.

Photon-Number Resolution in Conventional Superconducting Nanowire Single-Photon Detectors: Theoretical Predictions

High-dimensional (dimension d > 2) quantum key distribution (QKD) protocols that encode information in the temporal degree of freedom promise to overcome some of the challenges of qubit-based (d = 2) QKD systems. In particular, the long recovery time of single-photon detectors and large channel noise at long distance both limit the rate at which a final secure key can be generated in a low-dimension QKD system. We propose and demonstrate a practical discrete-variable time-frequency protocol with d = 4 at a wavelength of 1550 nm, where the temporal states are secured by transmitting and detecting their dual states under Fourier transformation, known as the frequency-basis states, augmented by a decoy-state protocol. We show that the discrete temporal and frequency states can be generated and detected using commercially-available equipment with high timing and spectral efficiency. In our initial experiments, we only have access to detectors that have low efficiency (1%) at 1550 nm. Together with other component losses, our system is equivalent to a QKD system with ideal components and a 50-km-long optical-fiber quantum channel. We find that our system maintains a spectral visibility of over 99.0% with a quantum bit error rate of 2.3%, which is largely due to the finite extinction ratio of the intensity modulators used in the transmitter. The estimated secure key rate of this system is 7.7×104 KHz, which should improve drastically when we use detectors optimized for 1550 nm.