High-dimensional Quantum Key Distribution Research Articles

High-dimensional quantum key distribution with the entangled single-photon-added coherent state

High-dimensional quantum key distribution (HD-QKD) can generate more secure bits for one detection event so that it can achieve long distance key distribution with a high secret key capacity. In this Letter, we present a decoy state HD-QKD scheme with the entangled single-photon-added coherent state (ESPACS) source. We present two tight formulas to estimate the single-photon fraction of postselected events and Eve's Holevo information and derive lower bounds on the secret key capacity and the secret key rate of our protocol. We also present finite-key analysis for our protocol by using the Chernoff bound. Our numerical results show that our protocol using one decoy state can perform better than that of previous HD-QKD protocol with the spontaneous parametric down conversion (SPDC) using two decoy states. Moreover, when considering finite resources, the advantage is more obvious.

Finite-key analysis for time-energy high-dimensional quantum key distribution

Time-energy high-dimensional quantum key distribution (HD-QKD) leverages the high-dimensional nature of time-energy entangled biphotons and the loss tolerance of single-photon detection to achieve long-distance key distribution with high photon information efficiency. To date, the general-attack security of HD-QKD has only been proven in the asymptotic regime, while HD-QKD's finite-key security has only been established for a limited set of attacks. Here we fill this gap by providing a rigorous HD-QKD security proof for general attacks in the finite-key regime. Our proof relies on an entropic uncertainty relation that we derive for time and conjugate-time measurements that use dispersive optics, and our analysis includes an efficient decoy-state protocol in its parameter estimation. We present numerically evaluated secret-key rates illustrating the feasibility of secure and composable HD-QKD over metropolitan-area distances when the system is subjected to the most powerful eavesdropping attack.

The information of high-dimensional time-bin encoded photons

We determine the shared information that can be extracted from time-bin entangled photons using frame encoding. We consider photons generated by a general down-conversion source and also model losses, dark counts and the effects of multiple photons within each frame. Furthermore, we describe a procedure for including other imperfections such as after-pulsing, detector dead-times and jitter. The results are illustrated by deriving analytic expressions for the maximum information that can be extracted from high-dimensional time-bin entangled photons generated by a spontaneous parametric down conversion. A key finding is that under realistic conditions and using standard SPAD detectors one can still choose frame size so as to extract over 10 bits per photon. These results are thus useful for experiments on high-dimensional quantum-key distribution system.

Detector-decoy high-dimensional quantum key distribution.

The decoy-state high-dimensional quantum key distribution provides a practical secure way to share more private information with high photon-information efficiency. In this paper, based on detector-decoy method, we propose a detector-decoy high-dimensional quantum key distribution protocol. Employing threshold detectors and a variable attenuator, we can promise the security under Gsussian collective attacks with much simpler operations in practical implementation. By numerical evaluation, we show that without varying the source intensity, our protocol performs much better than one-decoy-state protocol and as well as the two-decoy-state protocol in the infinite-size regime. In the finite-size regime, our protocol can achieve better results. Specially, when the detector efficiency is lower, the advantage of the detector-decoy method becomes more prominent.

Finite-key analysis of a practical decoy-state high-dimensional quantum key distribution

Compared with two-level quantum key distribution (QKD), high-dimensional QKD enables two distant parties to share a secret key at a higher rate. We provide a finite-key security analysis for the recently proposed practical high-dimensional decoy-state QKD protocol based on time-energy entanglement. We employ two methods to estimate the statistical fluctuation of the postselection probability and give a tighter bound on the secure-key capacity. By numerical evaluation, we show the finite-key effect on the secure-key capacity in different conditions. Moreover, our approach could be used to optimize parameters in practical implementations of high-dimensional QKD.

Orbital angular momentum vertical-cavity surface-emitting lasers

Harnessing the orbital angular momentum (OAM) of light is an appealing approach to developing photonic technologies for future applications in optical communications and high-dimensional quantum key distribution (QKD) systems. An outstanding challenge to the widespread uptake of the OAM resource is its efficient generation. In this work we design a new device that can directly emit an OAM-carrying light beam from a low-cost semiconductor laser. By fabricating micro-scale spiral phase plates within the aperture of a vertical-cavity surface-emitting laser (VCSEL), the linearly polarized Gaussian beam emitted by the VCSEL is converted into a beam carrying specific OAM modes and their superposition states, with high efficiency and high beam quality. This new approach to OAM generation may be particularly useful in the field of OAM-based optical and quantum communications, especially for short-reach data interconnects and QKD.

High-dimensional quantum cryptography with twisted light

Quantum key distribution (QKD) systems often rely on polarization of light for encoding, thus limiting the amount of information that can be sent per photon and placing tight bounds on the error rates that such a system can tolerate. Here we describe a proof-of-principle experiment that indicates the feasibility of high-dimensional QKD based on the transverse structure of the light field allowing for the transfer of more than 1 bit per photon. Our implementation uses the orbital angular momentum (OAM) of photons and the corresponding mutually unbiased basis of angular position (ANG). Our experiment uses a digital micro-mirror device for the rapid generation of OAM and ANG modes at 4 kHz, and a mode sorter capable of sorting single photons based on their OAM and ANG content with a separation efficiency of 93%. Through the use of a seven-dimensional alphabet encoded in the OAM and ANG bases, we achieve a channel capacity of 2.05 bits per sifted photon. Our experiment demonstrates that, in addition to having an increased information capacity, multilevel QKD systems based on spatial-mode encoding can be more resilient against intercept-resend eavesdropping attacks.

Practical high-dimensional quantum key distribution with decoy states

High-dimensional quantum key distribution (HD-QKD) allows two parties to generate multiple secure bits of information per detected photon. In this work, we show that decoy state protocols can be practically implemented for HD-QKD using only one or two decoy states. HD-QKD with two decoy states, under realistic experimental constraints, can generate multiple secure bits per coincidence at distances over 200 km and at rates similar to those achieved by a protocol with infinite decoy states. Furthermore, HD-QKD with only one decoy state is practical at short distances, where it is almost as secure as a protocol with two decoy states. HD-QKD with only one or two decoy states can therefore be implemented to optimize the rate of secure quantum communications.

Cavity-enabled high-dimensional quantum key distribution

High-dimensional quantum key distribution (QKD) offers the possibility of encoding multiple bits of key on a single entangled photon pair. An experimentally promising approach to realizing this is to use energy–time entanglement. Currently, however, the control of very high-dimensional entangled photons is challenging. We present a simple and experimentally compact approach, which is based on a cavity that allows one to measure two different bases: the time of arrival and another that is approximately mutually unbiased to the arrival time. We quantify the errors in the setup, due both to the approximate nature of the mutually unbiased measurement and as a result of experimental errors. It is shown that the protocol can be adapted using a cut-off so that it is robust against the considered errors, even within the regime of up to 10 bits per photon pair.

Unconditional security of time-energy entanglement quantum key distribution using dual-basis interferometry.

High-dimensional quantum key distribution (HDQKD) offers the possibility of high secure-key rate with high photon-information efficiency. We consider HDQKD based on the time-energy entanglement produced by spontaneous parametric down-conversion and show that it is secure against collective attacks. Its security rests upon visibility data-obtained from Franson and conjugate-Franson interferometers-that probe photon-pair frequency correlations and arrival-time correlations. From these measurements, an upper bound can be established on the eavesdropper's Holevo information by translating the Gaussian-state security analysis for continuous-variable quantum key distribution so that it applies to our protocol. We show that visibility data from just the Franson interferometer provides a weaker, but nonetheless useful, secure-key rate lower bound. To handle multiple-pair emissions, we incorporate the decoy-state approach into our protocol. Our results show that over a 200-km transmission distance in optical fiber, time-energy entanglement HDQKD could permit a 700-bit/sec secure-key rate and a photon information efficiency of 2 secure-key bits per photon coincidence in the key-generation phase using receivers with a 15% system efficiency.

Free-space communication through turbulence: a comparison of plane-wave and orbital-angular-momentum encodings

Free-space communication allows one to use spatial mode encoding, which is susceptible to the effects of diffraction and turbulence. Here, we discuss the optimum communication modes of a system while taking such effects into account. We construct a free-space communication system that encodes information onto the plane-wave (PW) modes of light. We study the performance of this system in the presence of atmospheric turbulence, and compare it with previous results for a system employing orbital-angular-momentum (OAM) encoding. We are able to show that the PW basis is the preferred basis set for communication through atmospheric turbulence for a system with a large Fresnel number product. This study has important implications for high-dimensional quantum key distribution systems.

Quantum key distribution session with 16-dimensional photonic states

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD.

High-dimensional quantum key distribution using dispersive optics

We propose a high-dimensional quantum key distribution (QKD) protocol that employs temporal correlations of entangled photons. The security of the protocol relies on measurements by Alice and Bob in one of two conjugate bases, implemented using dispersive optics. We show that this dispersion-based approach is secure against general coherent attacks. The protocol is additionally compatible with standard fiber telecommunications channels and wavelength division multiplexers. We offer multiple implementations to enhance the transmission rate and describe a heralded qudit source that is easy to implement and enables secret-key generation at up to 100 Mbps at over 2 bits per photon.

Security of high-dimensional quantum key distribution protocols using Franson interferometers

Franson interferometers are increasingly being proposed as a means of securing high-dimensional energy–time entanglement-based quantum key distribution (QKD) systems. Heuristic arguments have been proposed that purport to demonstrate the security of these schemes. We show, however, that such systems are vulnerable to attacks that localize the photons to several temporally separate locations. This demonstrates that a single pair of Franson interferometers is not a practical approach to securing high-dimensional energy–time entanglement-based QKD. This observation leads us to investigate the security of modified Franson-based-protocols, where Alice and Bob have two or more Franson interferometers. We show that such setups can improve the sensitivity against attacks that localize the photons to multiple temporal locations. While our results do not constitute a full security proof, they do show that a single pair of Franson interferometers is not secure and that multiple such interferometers could be a promising candidate for experimentally realizable high-dimensional QKD.

Efficient single-spatial-mode periodically-poled KTiOPO_4 waveguide source for high-dimensional entanglement-based quantum key distribution

We demonstrate generation of high-purity photon pairs at 1560 nm in a single spatial mode from a periodically-poled KTiOPO_4 (PPKTP) waveguide. With nearly lossless spectral filtering, the PPKTP waveguide source shows approximately 80 % single-mode fiber coupling efficiency and is well suited for high-dimensional time-energy entanglement-based quantum key distribution. Using high-count-rate self-differencing InGaAs single-photon avalanche photodiodes configured with either square or sinusoidal gating, we achieve > 1 Mbit/s raw key generation with 3 bits-per-photon encoding, and, to the best of our knowledge, the highest reported Franson quantum-interference visibility of 98.2 % without subtraction of accidental coincidences.

Near-perfect sorting of orbital angular momentum and angular position states of light

We present a novel method for efficient sorting of photons prepared in states of orbital angular momentum (OAM) and angular position (ANG). A log-polar optical transform is used in combination with a holographic beam-splitting method to achieve better mode discrimination and reduced cross-talk than reported previously. Simulating this method for 7 modes, we have calculated an improved mutual information of 2.43 bits/photon and 2.29 bits/photon for OAM and ANG modes respectively. In addition, we present preliminary results from an experimental implementation of this technique. This method is expected to have important applications for high-dimensional quantum key distribution systems.

Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding

We describe an experimental implementation of a free-space 11-dimensional communication system using orbital angular momentum (OAM) modes. This system has a maximum measured OAM channel capacity of 2.12 bits/photon. The effects of Kolmogorov thin-phase turbulence on the OAM channel capacity are quantified. We find that increasing the turbulence leads to a degradation of the channel capacity. We are able to mitigate the effects of turbulence by increasing the spacing between detected OAM modes. This study has implications for high-dimensional quantum key distribution (QKD) systems. We describe the sort of QKD system that could be built using our current technology.

High-dimensional entanglement for long distance quantum communication

In this paper, we provide a scheme to generate a high-dimensional entanglement source for long distance quantum communication. We utilize a continuous wave pump laser to produce polarization-time two-body four-dimensional entangled photon pairs. Under 20 mW of pump power, we achieve 700 entangled photon pairs per second with a fidelity of 89%±3%. Compared with other known high dimension entangled sources, the developed source in the paper is easy to transmit over a long distance and its phase stability is easy to achieve. Therefore, the source is more suited for the future long distance high-dimensional quantum communication tasks and testing the quantum nonlocality, for example, long distance high dimensional quantum key distribution, experimental testing two-particle Greenberger-Horne-Zeilinger theorem, implementation of two-particle quantum pseudo telepathy, etc.

Six-State Quantum Key Distribution Using Photons with Orbital Angular Momentum

A new implementation of high-dimensional quantum key distribution (QKD) protocol is discussed. Using three mutual unbiased bases, we present a d-level six-state QKD protocol that exploits the orbital angular momentum with the spatial mode of the light beam. The protocol shows that the feature of a high capacity since keys are encoded using photon modes in d-level Hilbert space. The devices for state preparation and measurement are also discussed. This protocol has high security and the alignment of shared reference frames is not needed between sender and receiver.

Holographic generation of complex fields with spatial light modulators: application to quantum key distribution

There has been considerable interest recently in the generation of azimuthal phase functions associated with photon orbital angular momentum (OAM) for high-dimensional quantum key distribution. The generation of secure quantum keys requires not only this pure phase basis but also additional bases comprised of orthonormal superposition states formed from the pure states. These bases are also known as mutually unbiased bases (MUBs) and include quantum states whose wave functions are modulated in both phase and amplitude. Although modulo 2pi optical path control with high-resolution spatial light modulators (SLMs) is well suited to creating the azimuthal phases associated with the pure states, it does not introduce the amplitude modulation associated with the MUB superposition states. Using computer-generated holography (CGH) with the Leith-Upatnieks approach to hologram recording, however, both phase and amplitude modulation can be achieved. We present a description of the OAM states of a three-dimensional MUB system and analyze the construction of these states via CGH with a phase-modulating SLM. The effects of phase holography artifacts on quantum-state generation are quantified and a prescription for avoiding these artifacts by preconditioning the hologram function is presented. Practical effects associated with spatially isolating the first-order diffracted field are also quantified, and a demonstration utilizing a liquid-crystal SLM is presented.