Quantum key distribution session with 16-dimensional photonic states

Pathways for Entanglement-Based Quantum Communication in the Face of High Noise

Entanglement-based quantum communication offers an increased level of security in practical secret shared key distribution. One of the fundamental principles enabling this security-the fact that interfering with one photon will destroy entanglement and thus be detectable-is also the greatest obstacle. Random encounters of traveling photons, losses, and technical imperfections make noise an inevitable part of any quantum communication scheme, severely limiting distance, key rate, and environmental conditions in which quantum key distribution can be employed. Using photons entangled in their spatial degree of freedom, we show that the increased noise resistance of high-dimensional entanglement can indeed be harnessed for practical key distribution schemes. We perform quantum key distribution in eight entangled paths at various levels of environmental noise and show key rates that, even after error correction and privacy amplification, still exceed 1 bit per photon pair and furthermore certify a secure key at noise levels that would prohibit comparable qubit based schemes from working.

Engineering spatial correlations of entangled photon pairs by pump beam shaping

The ability to engineer the properties of quantum optical states is essential for quantum information processing applications. Here, we demonstrate tunable control of spatial correlations between photon pairs produced by spontaneous parametric down-conversion, and measure them using an electron multiplying charge coupled device (EMCCD) camera. By shaping the spatial pump beam profile in a type-I collinear configuration, we tailor the spatial structure of coincidences between photon pairs entangled in high dimensions without effect on intensity. The results highlight fundamental aspects of spatial coherence and hold potential for the development of quantum technologies based on high-dimensional spatial entanglement.

Performance analysis of free-space quantum key distribution using multiple spatial modes

In the diffraction-limited near-field propagation regime, free-space optical quantum key distribution (QKD) systems can employ multiple spatial modes to improve their key rate. This improvement can be effected by means of high-dimensional QKD or by spatial-mode multiplexing of independent QKD channels, with the latter, in general, offering higher key rates. Here, we theoretically analyze spatial-mode-multiplexed, decoy-state BB84 whose transmitter mode set is either a collection of phase-tilted, flat-top focused beams (FBs) or the Laguerre-Gaussian (LG) modes. Although for vacuum propagation the FBs suffer a QKD rate penalty relative to the LG modes, their potential ease of implementation make them an attractive alternative. Moreover, in the presence of turbulence, the FB modes may outperform the LG modes.

Adaptable transmitter for discrete and continuous variable quantum key distribution

We present a versatile transmitter capable of performing both discrete variable and continuous variable quantum key distribution protocols (DV-QKD and CV-QKD, respectively). Using this transmitter, we implement a time-bin encoded BB84 DV-QKD protocol over a physical quantum channel of 47 km and a GG02 CV-QKD protocol with true local oscillator over a 10.5 km channel, achieving secret key rates of 4.1 kbps and 1 Mbps for DV- and CV-QKD, respectively. The reported transmitter scheme is particularly suitable for re-configurable optical networks where the QKD protocol is selected to optimize the performance according to the parameters of the links.

Control over the transverse structure and long-distance fiber propagation of light at the single-photon level

Quantum entanglement is arguably the cornerstone which differentiates the quantum realm from its classical counterpart. While entanglement can reside in any photonic degree of freedom, polarization permits perhaps the most straightforward manipulation due to the widespread availability of standard optical elements such as waveplates and polarizers. As a step towards a fuller exploitation of entanglement in other degrees of freedom, in this work we demonstrate control over the transverse spatial structure of light at the single-photon level. In particular we integrate in our setup all the technologies required for: (i) fibre-based photon pair generation, (ii) deterministic and broadband single-photon spatial conversion relying on a passive optical device, and (iii) single-photon transmission, while retaining transverse structure, over 400 m of few-mode fibre. In our experiment, we employ a mode selective photonic lantern multiplexer with the help of which we can convert the transverse profile of a single photon from the fundamental mode into any of the supported higher-order modes. We also achieve conversion to an incoherent or coherent addition of two user-selected higher order modes by addressing different combinations of inputs in the photonic lantern multiplexer. The coherent nature of the addition, and extraction of usable orbital angular momentum at the single-photon level, is further demonstrated by far-field diffraction through a triangular aperture. Our work could enable studies of photonic entanglement in the transverse modes of a fibre and could constitute a key resource quantum for key distribution with an alphabet of scalable dimension.

Stochastic optimization on complex variables and pure-state quantum tomography

Real-valued functions of complex arguments violate the Cauchy-Riemann conditions and, consequently, do not have Taylor series expansion. Therefore, optimization methods based on derivatives cannot be directly applied to this class of functions. This is circumvented by mapping the problem to the field of the real numbers by considering real and imaginary parts of the complex arguments as the new independent variables. We introduce a stochastic optimization method that works within the field of the complex numbers. This has two advantages: Equations on complex arguments are simpler and easy to analyze and the use of the complex structure leads to performance improvements. The method produces a sequence of estimates that converges asymptotically in mean to the optimizer. Each estimate is generated by evaluating the target function at two different randomly chosen points. Thereby, the method allows the optimization of functions with unknown parameters. Furthermore, the method exhibits a large performance enhancement. This is demonstrated by comparing its performance with other algorithms in the case of quantum tomography of pure states. The method provides solutions which can be two orders of magnitude closer to the true minima or achieve similar results as other methods but with three orders of magnitude less resources.

Phase Matching Quantum Key Distribution based on Single-Photon Entanglement

Two time-reversal quantum key distribution (QKD) schemes are the quantum entanglement based device-independent (DI)-QKD and measurement-device-independent (MDI)-QKD. The recently proposed twin field (TF)-QKD, also known as phase-matching (PM)-QKD, has improved the key rate bound from O(η) to O[Formula: see text] with η the channel transmittance. In fact, TF-QKD is a kind of MDI-QKD but based on single-photon detection. In this paper, we propose a different PM-QKD based on single-photon entanglement, referred to as single-photon entanglement-based phase-matching (SEPM)-QKD, which can be viewed as a time-reversed version of the TF-QKD. Detection loopholes of the standard Bell test, which often occur in DI-QKD over long transmission distances, are not present in this protocol because the measurement settings and key information are the same quantity which is encoded in the local weak coherent state. We give a security proof of SEPM-QKD and demonstrate in theory that it is secure against all collective attacks and beam-splitting attacks. The simulation results show that the key rate enjoys a bound of O[Formula: see text] with respect to the transmittance. SEPM-QKD not only helps us understand TF-QKD more deeply, but also hints at a feasible approach to eliminate detection loopholes in DI-QKD for long-distance communications.

Large-alphabet encoding for higher-rate quantum key distribution

The manipulation of high-dimensional degrees of freedom provides new opportunities for more efficient quantum information processing. It has recently been shown that high-dimensional encoded states can provide significant advantages over binary quantum states in applications of quantum computation and quantum communication. In particular, high-dimensional quantum key distribution enables higher secret-key generation rates under practical limitations of detectors or light sources, as well as greater error tolerance. Here, we demonstrate high-dimensional quantum key distribution capabilities both in the laboratory and over a deployed fiber, using photons encoded in a high-dimensional alphabet to increase the secure information yield per detected photon. By adjusting the alphabet size, it is possible to mitigate the effects of receiver bottlenecks and optimize the secret-key rates for different channel losses. This work presents a strategy for achieving higher secret-key rates in receiver-limited scenarios and marks an important step toward high-dimensional quantum communication in deployed fiber networks.

Self-healing high-dimensional quantum key distribution using hybrid spin-orbit Bessel states

Using spatial modes for quantum key distribution (QKD) has become highly topical due to their infinite dimensionality, promising high information capacity per photon. However, spatial distortions reduce the feasible secret key rates and compromise the security of a quantum channel. In an extreme form such a distortion might be a physical obstacle, impeding line-of-sight for free-space channels. Here, by controlling the radial degree of freedom of a photon's spatial mode, we are able to demonstrate hybrid high-dimensional QKD through obstacles with self-reconstructing single photons. We construct high-dimensional mutually unbiased bases using spin-orbit hybrid states that are radially modulated with a non-diffracting Bessel-Gaussian (BG) profile, and show secure transmission through partially obstructed quantum links. Using a prepare-measure protocol we report higher quantum state self-reconstruction and information retention for the non-diffracting BG modes as compared to Laguerre-Gaussian modes, obtaining a quantum bit error rate (QBER) that is up to 3× lower. This work highlights the importance of controlling the radial mode of single photons in quantum information processing and communication as well as the advantages of QKD with hybrid states.

Optimized channel allocation scheme for jointly reducing four-wave mixing and Raman scattering in the DWDM-QKD system

Conducting quantum key distribution (QKD) through existing optical fibers together with conventional communication signals is a viable way to expand its practical application, but weak quantum signals can be severely disrupted by co-propagating classical signals. In this paper, the suppression of four-wave mixing (FWM) noise and Raman noise is considered simultaneously for the first time, to the best of our knowledge, and the joint optimized channel allocation (JOCA) scheme is proposed. In the JOCA scheme, the quantum channels and classical channels are interleaved with each other to avoid FWM noise and optimal quantum channel positions are chosen in variable conditions according to the Raman scattering spectrum. Experimental measurements of the noise photons show that the JOCA scheme can effectively reduce the impairments on quantum signals compared with the single-target schemes. Additionally, simulation results verify that the JOCA scheme can increase the secure key generation rate and transmission distance, and that it also enables the DWDM-QKD system to tolerate higher-power classical signals and more classical channels, which improve the compatibility with a high-capacity communication system.

Characterizing d-dimensional quantum channels by means of quantum process tomography

In this Letter, we propose a simple optical architecture based on phase-only programmable spatial light modulators, in order to characterize general processes on photonic spatial quantum systems in a d>2 Hilbert space. We demonstrate the full reconstruction of typical noises affecting quantum computing, such as amplitude shifts, phase shifts, and depolarizing channels in dimension d=5. We have also reconstructed simulated atmospheric turbulences affecting a free-space transmission of qudits in dimension d=4. In each case, quantum process tomography was performed in order to obtain the matrix χ that fully describes the corresponding quantum channel, E. Fidelities between the states are experimentally obtained after going through the channel, and the expected ones are above 97%.

Certifying an Irreducible 1024-Dimensional Photonic State Using Refined Dimension Witnesses

We report on a new class of dimension witnesses, based on quantum random access codes, which are a function of the recorded statistics and that have different bounds for all possible decompositions of a high-dimensional physical system. Thus, it certifies the dimension of the system and has the new distinct feature of identifying whether the high-dimensional system is decomposable in terms of lower dimensional subsystems. To demonstrate the practicability of this technique, we used it to experimentally certify the generation of an irreducible 1024-dimensional photonic quantum state. Therefore, certifying that the state is not multipartite or encoded using noncoupled different degrees of freedom of a single photon. Our protocol should find applications in a broad class of modern quantum information experiments addressing the generation of high-dimensional quantum systems, where quantum tomography may become intractable.

Direct Generation and Detection of Quantum Correlated Photons with 3.2 um Wavelength Spacing

Quantum correlated, highly non-degenerate photons can be used to synthesize disparate quantum nodes and link quantum processing over incompatible wavelengths, thereby constructing heterogeneous quantum systems for otherwise unattainable superior performance. Existing techniques for correlated photons have been concentrated in the visible and near-IR domains, with the photon pairs residing within one micron. Here, we demonstrate direct generation and detection of high-purity photon pairs at room temperature with 3.2 um wavelength spacing, one at 780 nm to match the rubidium D2 line, and the other at 3950 nm that falls in a transparent, low-scattering optical window for free space applications. The pairs are created via spontaneous parametric downconversion in a lithium niobate waveguide with specially designed geometry and periodic poling. The 780 nm photons are measured with a silicon avalanche photodiode, and the 3950 nm photons are measured with an upconversion photon detector using a similar waveguide, which attains 34% internal conversion efficiency. Quantum correlation measurement yields a high coincidence-to-accidental ratio of 54, which indicates the strong correlation with the extremely non-degenerate photon pairs. Our system bridges existing quantum technology to the challenging mid-IR regime, where unprecedented applications are expected in quantum metrology and sensing, quantum communications, medical diagnostics, and so on.

Generation of two pairs of qudits using four photons and a single degree of freedom

Qudits, d-level quantum systems, have been shown to provide a better resource for quantum key distribution and other Quantum Information protocols. It is customary to generate photonic qudits using more than one degree of freedom of the same photon. In much the same way, multi-qubit states are generated using only a pair of photons and ingenious ways to manipulate more than one degree of freedom independently. In contrast to such costly implementations in terms of quantum resources, we present the controlled generation of two copies of two-qudit states using four photons and a single degree of freedom, transverse momentum. The degree of entanglement within each pair was inferred by exploiting the availability of two copies of the same state, without the need of a full tomographic reconstruction of the states, and both highly-entangled and separable states were generated. We show theoretically that the set of states obtainable using our setup is very diverse, ranging from maximally entangled states of qudits to separable states.

N-dimensional measurement-device-independent quantum key distribution with N + 1 un-characterized sources: zero quantum-bit-error-rate case

We study N-dimensional measurement-device-independent quantum-key-distribution protocol where one checking state is used. Only assuming that the checking state is a superposition of other N sources, we show that the protocol is secure in zero quantum-bit-error-rate case, suggesting possibility of the protocol. The method may be applied in other quantum information processing.

Privacy Preserving Quantum Anonymous Transmission via Entanglement Relay

Anonymous transmission is an interesting and crucial issue in computer communication area, which plays a supplementary role to data privacy. In this paper, we put forward a privacy preserving quantum anonymous transmission protocol based on entanglement relay, which constructs anonymous entanglement from EPR pairs instead of multi-particle entangled state, e.g. GHZ state. Our protocol achieves both sender anonymity and receiver anonymity against an active adversary and tolerates any number of corrupt participants. Meanwhile, our protocol obtains an improvement in efficiency compared to quantum schemes in previous literature.

Five Measurement Bases Determine Pure Quantum States on Any Dimension

A long-standing problem in quantum mechanics is the minimum number of observables required for the characterization of unknown pure quantum states. The solution to this problem is especially important for the developing field of high-dimensional quantum information processing. In this work we demonstrate that any pure d-dimensional state is unambiguously reconstructed by measuring five observables, that is, via projective measurements onto the states of five orthonormal bases. Thus, in our method the total number of different measurement outcomes (5d) scales linearly with d. The state reconstruction is robust against experimental errors and requires simple postprocessing, regardless of d. We experimentally demonstrate the feasibility of our scheme through the reconstruction of eight-dimensional quantum states, encoded in the momentum of single photons.

Experimental Satellite Quantum Communications

Quantum communication (QC), namely, the faithful transmission of generic quantum states, is a key ingredient of quantum information science. Here we demonstrate QC with polarization encoding from space to ground by exploiting satellite corner cube retroreflectors as quantum transmitters in orbit and the Matera Laser Ranging Observatory of the Italian Space Agency in Matera, Italy, as a quantum receiver. The quantum bit error ratio (QBER) has been kept steadily low to a level suitable for several quantum information protocols, as the violation of Bell inequalities or quantum key distribution (QKD). Indeed, by taking data from different satellites, we demonstrate an average value of QBER=4.6% for a total link duration of 85 s. The mean photon number per pulse μ_{sat} leaving the satellites was estimated to be of the order of one. In addition, we propose a fully operational satellite QKD system by exploiting our communication scheme with orbiting retroreflectors equipped with a modulator, a very compact payload. Our scheme paves the way toward the implementation of a QC worldwide network leveraging existing receivers.

Practical quantum private query of blocks based on unbalanced-state Bennett-Brassard-1984 quantum-key-distribution protocol

Until now, the only kind of practical quantum private query (QPQ), quantum-key-distribution (QKD)-based QPQ, focuses on the retrieval of a single bit. In fact, meaningful message is generally composed of multiple adjacent bits (i.e., a multi-bit block). To obtain a message from database, the user Alice has to query l times to get each a_i. In this condition, the server Bob could gain Alice's privacy once he obtains the address she queried in any of the l queries, since each a_i contributes to the message Alice retrieves. Apparently, the longer the retrieved message is, the worse the user privacy becomes. To solve this problem, via an unbalanced-state technique and based on a variant of multi-level BB84 protocol, we present a protocol for QPQ of blocks, which allows the user to retrieve a multi-bit block from database in one query. Our protocol is somewhat like the high-dimension version of the first QKD-based QPQ protocol proposed by Jacobi et al., but some nontrivial modifications are necessary.

Applying the simplest Kochen-Specker set for quantum information processing

Kochen-Specker (KS) sets are key tools for proving some fundamental results in quantum theory and also have potential applications in quantum information processing. However, so far, their intrinsic complexity has prevented experimentalists from using them for any application. The KS set requiring the smallest number of contexts has been recently found. Relying on this simple KS set, here we report an input state-independent experimental technique to certify whether a set of measurements is actually accessing a preestablished quantum six-dimensional space encoded in the transverse momentum of single photons.

High speed switching between arbitrary spatial light profiles

Complex images, inscribed into the spatial profile of a laser beam or even a single photon, offer a highly efficient method of data encoding. Here we present a prototype system which can quickly modulate between arbitrary images. We display an array of holograms, each defined by its phase and intensity profile, on a spatial light modulator. The input beam is then steered by an acousto-optic modulator to one of these holograms, where it is converted into the desired light mode. We demonstrate switching between characters within three separate alphabets at a switching rate of up to10 kHz. This rate is limited by our detection system, and we anticipate that the system is capable of far higher rates. Furthermore our system is not limited in efficiency by channel number, making it ideal for quantum communication applications.

Device-independent certification of high-dimensional quantum systems

An important problem in quantum information processing is the certification of the dimension of quantum systems without making assumptions about the devices used to prepare and measure them, that is, in a device-independent manner. A crucial question is whether such certification is experimentally feasible for high-dimensional quantum systems. Here we experimentally witness in a device-independent manner the generation of six-dimensional quantum systems encoded in the orbital angular momentum of single photons and show that the same method can be scaled, at least, up to dimension 13.

Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator

Spatial qudits are D-dimensional (D ≥ 2) quantum systems carrying information encoded in the discretized transverse momentum and position of single photons. We present a proof-of-principle demonstration of a method for preparing arbitrary pure states of such systems by using a single phase-only spatial light modulator (SLM). The method relies on the encoding of the complex transmission function corresponding to a given spatial qudit state onto a preset diffraction order of a phase-only grating function addressed at the SLM. Fidelities of preparation above 94% were obtained with this method, which is simpler, less costly, and more efficient than those that require two SLMs for the same purpose.