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Abstract
We present a new compact and robust polarization state transmitter designed to execute the BB84 quantum key distribution protocol. Our transmitter prepares polarization states using a single commercial-off-the-shelf phase modulator. Our scheme does not require global biasing to compensate thermal and mechanical drifts, as both of the system’s two time-demultiplexed polarization modes share a single optical path. Furthermore, the transmitter’s optical path entails a double-pass through the phase modulation device for each polarization mode, allowing multiple phase rotations to be impinged on each light pulse. We present a proof-of-concept prototype of this transmitter topology and demonstrate a mean intrinsic quantum bit error rate below 0.2% over a 5 hour measurement.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Secure communications are of paramount importance in the increasingly globalized world. Though traditional cryptographic protocols such as RSA were sufficient for protecting data systems for several decades [1], these protocols were designed with the assumption that potential adversaries lack the computational power to solve specific classes of mathematical problems. These standard cryptographic methods are thus vulnerable to advancements in machine computational power and to the potential development of key-breaking algorithms. In particular, it has been shown that quantum computers, which are expected to become commercially available in the next decade [2], will be able to efficiently solve the prime factorization and discrete logarithm problems upon which the most widely-used cryptographic protocols are based [1]. Such advancements have driven the development of “quantum-safe” encryption alternatives to standard cryptographic methods, such as quantum key distribution (QKD) [3] and post-quantum cryptography (PQC) [4].
Originally proposed by Bennet and Brassard in 1984, QKD encompasses a family of protocols that exploits the physics of quantum mechanics to ensure that cryptographic keys generated by these means are uncompromised by “eavesdropping” adversarial parties [5]. When combined with symmetric encryption methods such as the One-Time-Pad, QKD allows remote users to achieve information theoretically-secure communications. It is believed that combined implementations of both QKD and PQC will constitute standard security solutions in the future, as demonstrations have shown that the two cryptographic paradigms could be implemented in concert to provide an even higher degree of security [6].
The deployment of a full-scale QKD network for secure global communications will require the integration of several segments of network infrastructure, each of which will entail a unique set of characteristics and performance requirements. Numerous cryptographic protocols and key-generating devices have been developed to meet the specific constraints of each network segment [7,8]. QKD for metropolitan-access links will require a large number of low-cost, easy to install systems compatible with standard fiber optic communication infrastructure. Though continuous variable (CV) QKD systems are more conducive to sharing hardware infrastructure with classical signals [9], discrete variable (DV) QKD has higher loss tolerance and is thus more promising for mid-range inter-city segments (50-400 km) [10,11] and long-range satellite links (thousands of km) [12,13]. The QKD network nodes for these segments will be housed in difficult-to-access locations, such as big data centers, remote astronomical observatories, and satellites. This difficulty-of-access imposes stringent requirements on the robustness and durability of the key-generating devices, since repair missions will be expensive if not impossible. On-orbit systems in particular must adhere to strict constraints on total mass, volume and power consumption, and must be designed to maintain operations even in the adverse conditions of spaceflight [14,15]. Polarization state transmitters are among the more stable and durable QKD systems demonstrated experimentally, and are therefore a common choice for QKD systems subject to harsh environmental conditions [16]. In these systems, discrete-valued quantum states are encoded in the polarization degree of freedom (DoF) of light pulses. These information states are then transmitted over a channel, which can be either single mode optical fiber or free space depending on the application.
A popular approach to generating polarization-encoded quantum states involves the use of multiple lasers—e.g. one for each of the four states required for BB84 [13,17–21]. Though simple operationally, such designs are heavy and resource-demanding, and are therefore infeasible for use in full-scale deployed QKD networks. Moreover, multiple laser schemes are susceptible to side channel attacks based on potential distinguishabilities between light sources in wavelength [22], optical path [23], or pulse emission time [24]. Transmitters based on a single light source are thus preferred over multiple-source schemes. For single-source polarization state transmitters, all of the basis states required for the standard DV QKD protocols (such as BB84) are prepared with single phase modulation device.
Despite improvements in system complexity and security against side channel attacks, many of the proposed single-source solutions are prone to thermal fluctuations and mechanical stresses [25–27]. The resulting diminishment of transmitter performance can be mitigated with active temperature stabilization and bias control, but such environmental compensation mechanisms significantly increase the complexity and power consumption of transmission systems. Interestingly, different schemes have been proposed that have both a single light source and a disturbance-stable polarization encoding scheme. [28] proposes a transmitter free of temperature and bias controls, with intrinsic passive stability offered by a two-pass configuration in the optical path through a phase modulation device and a Faraday Mirror. The input polarization enters this transmitter at 45$^o$ with respect to the slow axis of the phase modulator (PhM), enabling the PhM to impinge relative phase rotations on both basis components of the input polarization. However, this scheme presents the disadvantage of requiring non-standard components and a high driving voltage, as the phase modulation is applied to both orthogonal polarization modes simultaneously. An alternative design using a polarization-maintaining Sagnac loop to generate polarization states is proposed and implemented in [29,30]. In this configuration, the orthogonal polarization modes traverse the loop in opposite directions, and each mode (separated in time) makes a single pass through the phase modulator. Despite using only standard components, these implementations still requires relatively high driving voltages as information states are only modulated in a single pass PhM pulse.
In this work we present a polarization modulation scheme based on a double-pass configuration of time-demultiplexed polarization modes through a lithium niobate phase modulation device. Our intrinsically stable design uses only standard components, and requires no active bias stabilization or temperature control. The system is designed to operate without bias or temperature control by exploiting the unique characteristics of Mach-Zehnder interferometers with polarization-maintaining fiber and the use of a Faraday mirror to compensate for polarization drift that arises in standard single mode fiber. By exploiting the polarization time-demultiplexing and the double pass configuration, the proposed transmitter is able to operate with lower modulation voltages than alternative polarization state transmission schemes.
2. Transmitter concept and design
With the objective of producing a QKD transmitter scheme suitable for operating in harsh environments, we prepare polarization states with a system that is stable over a long period of time and requires only minimal driving voltages, power consumption, and total system mass. In order to target these power and voltage goals, we introduce an optical topology in which laser pulses undergo two stages of phase modulation. By separating the polarization state preparation into multiple steps, we posit that the system presented will generate the full set of quantum states required for standard QKD protocols, but with a major savings in voltage and power consumption compared to single-pass and simultaneous polarization modulation designs.
We adhere to the BB84 protocol, which requires the transmitter to prepare quantum states in two mutually-unbiased two-state orthogonal bases $\{|{1}\rangle,|{2}\rangle\}$ and $\{|{3}\rangle,|{4}\rangle\}$, fulfilling the conjugate basis relations:
Figure 1 demonstrates the polarization state transmitter topology. The device can be divided into four constitutive blocks: (1) pulse generation, (2) initial polarization state preparation, (3) time demultiplexing, and (4) phase modulation. Faint optical pulses are generated in block 1 through direct current modulation of a DFB laser. The electrical laser-driving signal is generated by an electrical pulse generator (EPG). The pulses are attenuated to the desired level using a variable optical attenuator (VOA) and proceed to block 2 through polarization-maintaining fiber. In block 2, the initial polarization state is fixed in free space. Optical pulses are collimated into a free-space beam, wherein the polarization mode exiting the PM fiber slow axis is filtered using a linear polarizer (LP) and rotated with a half wave plate (HWP). The polarization state at block 2 output $|{\Psi _{t_0}\rangle}$ is set to be the diagonal state:
Following polarization-fixing in free space, optical pulses pass through a 50:50 beam splitter (BS), one of whose outputs is re-coupled into polarization-maintaining fiber, while the other output, which in principle can be used as a tap line for calibration purposes, is blocked for this demonstration.
Fig. 1. Scheme for the bias-free, low V$_{\pi }$ polarization transmitter and the detection unit used for its characterization. Polarization states are prepared in four consecutive stages: (1) optical pulse generation (at 1550 nm) , (2) initial polarization state preparation, (3) time de-multiplexing, and (4) phase modulation. The detection unit is based on SM fiber components (BS, PBS, MPC) and four single photon detectors connected to a TDC unit.
The optical pulses then enter block 3, in which the orthogonal components $|{H}\rangle$ and $|{V}\rangle$ are demultiplexed in time. The $|{D}\rangle$ pulse enters an unbalanced Mach-Zehnder interferometer (UMZI), which separates the pulse into $|{H}\rangle$ and $|{V}\rangle$ modes and adds a relative delay of $dt_{\text{UMZI}}$ to the $|{V}\rangle$ component (where $dt_{\text{UMZI}}$ must be larger than the width of the light pulses in time).
Following the UMZI time delay, the two polarization pulse components are re-combined into a single fiber with a PBS. The state exiting the time demultiplexing stage (block 3) can be represented as:
where the second element in the composite state kets denotes the orthogonal temporal modes of the pulses (0 or dt$_{\text{UMZI}}$). The resulting time demultiplexed pulses proceed through a single optical path into block 4 for phase modulation. In block 4, pulse components travel twice through a phase modulator (PhM); once on the “outbound” pass and a second time on the “return" pass. During each pass, the PhM impinges individual phase rotations onto each component pulse, with rotation magnitudes determined by the PhM driving voltage and both electro-optic coefficients of lithium niobate corresponding to each polarization. In the first pass, the $|{V}\rangle$ pulse acquires a phase of $\Delta \phi _1$ relative to the $|{H}\rangle$ component. The pulses are then reflected by a Faraday Mirror (FM) and pass back through the PhM, which impinges an additional relative phase of $\Delta \phi _2$ on the $|{V}\rangle$ pulse. Following the second pass of the pulses through the PhM, the full quantum state can be described as:The final output state of the system can be fully determined by the choice of $\Delta \Phi \:=\:\Delta \phi _1\:+\:\Delta \phi _2$, the net relative phase added to the $|{H}\rangle$ with respect to the $|{V}\rangle$ component. Other phase operations (such as the wave plate rotation in free space) contribute only to a net global phase, which is compensated during system startup calibration. By splitting the full phase rotation into two stages (the outbound and return passes), we decrease the maximum voltage required for polarization modulation by a factor of 2. That is to say, rather than rotating the full $\Delta \Phi$ with a single PhM pulse of voltage $V_{\Phi }$, we achieve the full ultimate phase rotation of $\Delta \Phi \:=\:\Delta \phi _1\:+\:\Delta \phi _2$ using two pulses of only $V \approx \frac {1}{2}V_{\Phi }$, as phase rotations scale linearly with PhM driving voltage.
Following the second round of phase modulation, each “return pass” pulse propagates back through block 3 along the opposite arm of the UMZI with respect to its “outbound" path. This effect arises from the phase rotation of $\phi _{FM}\:=\:\pi$ enacted by the FM, effectively changing $|{H}\rangle$ pulses to $|{V}\rangle$’s and vice-versa. As the pulse components exchange paths through the UMZI for the return pass, the time delay $\Delta t_{\text{UMZI}}$ (originally added to the first component pulse) is then enacted on the second component pulse $|{H}\rangle$. The interferometer is thus self-compensating, which eliminates the risk of additional time delay errors that could arise from diverging optical paths for each component pulse. The recombined light pulse emerging from the second pass through the UMZI with the desired polarization state can be expressed as:
After the return pass through block 3, pulses re-enter the block 2 free space module and are directed by the BS into the system detection module. The system output can be easily prepared as a free space beam or coupled into fiber depending on the desired application.
3. Transmitter characterization
A proof-of-principle prototype of the transmitter was developed to test the performance of the proposed scheme. Phase-randomized coherent pulses were generated by modulating a 1550 nm 10 GHz DFB laser diode from Gooch and Housego AA0701 (block 1 of Fig. 1). An electrical pulse amplifier (Minicircuits ZPUL-30P+) generated the laser driving signal, yielding optical pulses of 1 ns FWHM emitted at a repetition rate of $\sim 10 \:MHz$. The pulses were then attenuated to the single photon level using a manual VOA (IDIL COCOM00738).
The initial $|{D}\rangle$ state prepared in block 2 was directed into the UMZI, which generated a delay of $dt_{\text{UMZI}}=25\:ns$ between the $|{H}\rangle$ and $|{V}\rangle$ polarization components. The time de-multipexed pulses were then modulated by a 10 GHz phase modulator (IX blue MPZ-LN-10) and reflected by a Faraday mirror (FM). For the original prototype, a fiber delay line of 50 ns was placed before the FM to ensure that the second stage of modulation would occur only after both pulses completed their first pass through the phase modulator (PhM). This delay enabled a simple electronic driving signal pattern to be used to generate polarization states and allowed for clarity in the initial characterization.
An FPGA-based system-on-chip (SoC) design was developed to generate the required electrical driving and synchronization signals. The user can interact with the SoC by means of a Python UART API, which controls the synchronization signals and dinamically sends the desired data patterns to an on-board 1 GSPS digital-to-analog converter (see Supplement 1 for more details).
To characterize the single photon pulses, a fiber-based polarization receiver standard in BB84 implementations was used (Fig. 1). The receiver split the transmitted pulses into two channels with a 50-50 beam splitter. Each channel was then rotated into one of two mutually-unbiased detection bases using manual polarization controllers (MPCs). The MPC outputs were each routed into a PBS which separated the pulses into orthogonal components. The MPCs were configured such that the final four channels of the detection system contained the desired four polarization states. Each channel routed signals to an InGaAs/InP single photon avalanche diode detector (IDQube from IDQuantique).
We use the intrinsic quantum bit error rate (IQBER) as our primary metric for characterizing the purity and stability of each polarization state prepared by our source. The IQBER is given by:
where $|{\psi _A}\rangle$ represents the prepared polarization state under examination and $\langle{\psi _B^\bot }|$ is the detected orthogonal polarization state. One of the key benefits of the transmitter design presented is its low operating voltages. To determine the optimal voltage values for preparing each polarization state, the transmitter was configured to emit a single state while sweeping the modulation signal from -4 to 4 $V_{pp}$.Figure 2(b) shows the count rate for each detector for under different driving voltages $\Delta V_{pp}$. The effective $V_{\pi }$ was determined to be 3.7 $V$ for the current hardware configuration. Fig. 2(b) demonstrates that the unbiased relation is fulfilled for the states prepared by the transmitter. For each driving voltage at which the one basis state pair reaches maximum and minimum values, the two states in the conjugated basis present minimum bias.
Fig. 2. a) Electronic pulse sequence (blue) used to impinge the desired phase rotations on the horizontal and vertical polarization modes of the optical signal (red). b) Normalized transmission for each of the four polarization states under a sweep of driving PhM voltage. The effective $V_\pi$ of the device was determined to be 3.7 V. c) Intrinsic quantum bit error rates for each polarization state over a 5-hour measurement. States 1 and 2 (constituting the first polarization state basis) yield IQBERs of 0.27$\%$ and 0.13$\%$ while states 3 and 4 (comprising the second basis) have mean IQBER values of 0.21$\%$ and and 0.12$\%$ respectively. This figure corresponds to the first 5 hours of measurement from figure S3 in Supplement 1.
4. IQBER estimation and stability
The transmitter’s functionality and suitability for the BB84 protocol were demonstrated via characterization of the phase-modulated polarization state driving scheme. For each measurements, fixed patterns of polarization states were prepared and transmitted continuously to the detection system. The system’s stability was demonstrated through a long measurement (5 hours) of the intrinsic quantum bit error rates (IQBERs) of each of the four channels. Figure 2 c) shows the evolution of IQBER for each polarization state channel (based on 30-second measurements repeated continuously over the 5-hour integration period). The IQBERs remain remarkably low and unchanging over this window, and yield a mean IQBER of 0.18$\%$. Table 1 gives the mean IQBER and $\Delta V_{pp}= V_{dt_{\text{UMZI}}}$ for each polarization state obtained from the data in Fig. 2(c). Note that in Fig. 2 c), the $|{2}\rangle$ and $|{4}\rangle$ states exhibit a QBER lower than the two remaining states. This is due to the initial alignment process, which is performed by minimizing the error in the $|{2}\rangle$ and $|{4}\rangle$ states. In this way, any deviation in the orthogonality of the prepared and detected states affect only to the QBER of $|{1}\rangle$ and $|{3}\rangle$ states.
Table 1. Mean IQBER for each polarization state extracted from the 5 hour measurement. The values obtained for this measurement where 0.13$\%$, 0.12$\%$, 0.21$\%$, and 0.27$\%$. The $\Delta V_{pp}$ column gives the PhM driving voltage required to prepare each polarization state, with maximum value 3.1 V.
To determine the stability limit of the proposed scheme, we performed a 40-hour continuous measurement. The transmitter was programmed to prepare an initial set of control voltages for driving each state. The IQBERs measured using these driving voltages were compared to IQBERs measured using a second set of driving voltages that we updated continuously using an optimization algorithm to compensate for thermal drifts in the receiver. The mean IQBER using the thermal compensation optimization algorithm remained below 0.28$\%$ throughout the 40-hour measurement (see supplementary material). The eventual rise in IQBER over the 40-hour timescale can be attributed to slow thermal and mechanical stress fluctuations in the fiber-based receiver (for more information, see Supplement 1).
5. Discussion
We have presented a scheme for an intrinsically-stable polarization state transmitter for QKD. Beyond the thermal and mechanical stability of the system, we also demonstrated that with the double-pass configuration and the time de-multiplexing step, the system can be driven at significantly lower operating voltages than alternative transmitter topologies. It is worth mentioning that it is possible to achieve low state preparation voltages by doubling the number of active devices used for phase modulation. Instead, in our design this is achieved by a single modulator. A lower operating voltage comes at the cost of limiting the repetition rate of the system, since for each emitted symbol, the time required to establish a polarization state is four times longer than the duration of the optical pulse (compared with a factor of two of the bias-free schemes [28–30] or a single pulse-width in [26,27]). Our proof-of-concept demonstration of the proposed scheme yields a low IQBER for the polarization states and long-term stability with no detectable fluctuation over several hours. At present, the precision of system characterizations is limited by the stability of the detection system, which for this demonstration was implemented in standard SM fiber. Additionally, the present implementation of the transmitter design generated a repetition rate of 10 MHz, but the timing of this configuration can be optimized to achieve repetition rates close to 1 GHz using the same opto-electronic active components and higher bandwidth electrical amplifiers. A few simple alterations to the delay line lengths would also decrease the propagation times through the system and re-order the pulses in such a way that the PhM driving signal rate could be increased substantially. The presented design is also compatible with drift-free intensity modulator schemes for performing decoy-state QKD protocols [31], which constitutes a promising potential direction for using QKD polarization-encoding devices in harsh environments.
Funding
Ministerio de Ciencia e Innovación with funding from European Union NextGenerationEU (PRTR-C17.I1); Direcció General de Recerca, Generalitat de Catalunya NextGeneration Catalonia (CEX2019-000910-S); Fundación Cellex; FUNDACIÓ Privada MIR-PUIG; Generalitat de Catalunya through Centres de Recerca de Catalunya; Agència de Gestió d'Ajuts Universitaris i de Recerca (2021 SGR 01458).
Disclosures
AS, IL, and VP are co-inventors of a patent application related to the content of this paper.
Data Availability
Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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