⚛️ quantum physics

Demonstration of a partial knowledge quantum key distribution protocol

This paper presents a novel high-dimensional quantum key distribution protocol called \texttt{Bridge[ $d,q$ ]}, which generalizes \texttt{SARG04} to allow key distillation from partial knowledge, and experimentally demonstrates the \texttt{Bridge[$2,3$]} variant using a single Pockels cell for fast polarization switching.

Original author: Liran Shirizly, Leonid Vidro, Hagai S. Eisenberg

Published 2026-11-10

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CC BY 4.0

Original author: Liran Shirizly, Leonid Vidro, Hagai S. Eisenberg

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the author. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of secure communication, there is a fundamental promise: that two people can share a secret code that is physically impossible for a third party to intercept without being noticed. This promise relies on the strange rules of quantum mechanics, where the act of looking at a particle changes it. For decades, the standard way to build these codes has been to send particles of light, called photons, where the sender and receiver agree on a specific set of directions to measure them. If they happen to choose the same direction, they get a matching result, and that match becomes part of their secret key. The assumption has always been that to get a good key, both parties need to know exactly what the other person measured.

However, nature often offers more subtle possibilities. Sometimes, a measurement does not reveal the full story of a particle's state but instead rules out certain possibilities, leaving the observer with only partial information. It is like being told a card is not a heart; you do not know exactly which card it is, but you know it is not one of thirteen specific options. Scientists have long wondered if this kind of "partial knowledge" could still be used to build a secure communication line. If two people can agree on a secret even when they only know what the other person didn't do, it could open up new ways to protect data, especially in situations where perfect information is hard to get or where the usual methods are too slow or complex.

A team of researchers at the Hebrew University of Jerusalem has now taken a major step toward proving this idea works in the real world. They demonstrated a new method for creating secret keys, which they call the Bridge protocol, using a setup that allows them to share information even when they only have partial knowledge of each other's choices. In their experiment, the two parties, traditionally named Alice and Bob, sent photons to each other using three different sets of measurement directions, rather than the usual two. When they compared notes, they found that even though they could not always tell exactly which direction the other person had chosen, the information they did share was enough to distill a secure, mutual secret key. This is a significant shift from previous methods, where the goal was to ensure both parties had identical, complete information about every single bit of data.

The researchers built a physical device to test this concept, using a laser that fires tiny pulses of light. To create the necessary variety of directions, they used a special crystal that can twist the polarization of light, which is essentially the direction in which the light waves vibrate. A clever feature of their design was the use of a single crystal to switch between three different measurement directions. The light traveled through the crystal, bounced off a mirror, and traveled through it again. By carefully timing the electrical signals sent to the crystal, the researchers could ensure that the light was rotated differently on its way out than on its way back. This allowed them to simulate two different people making different choices using just one piece of equipment, simplifying the setup significantly.

In their experiment, the team showed that the system worked with high precision. They measured the light after it passed through the crystal and found that the directions were accurate, with the light vibrating in the intended orientations about 97 percent of the time. When they ran the full protocol, they calculated the rate at which they could generate a secure key. Even with the small amount of noise and error present in any real-world laboratory, they were able to extract a secure key at a rate of about 200 bits per second. This number is not just a theoretical possibility; it was a direct measurement from their working device. The results confirmed that the protocol is robust enough to handle the imperfections of a real environment, provided the error rate stays below a specific threshold, which their system comfortably met.

The significance of this work goes beyond just creating a new type of key. It demonstrates that secure communication does not require perfect, full knowledge of the other person's actions. In the new Bridge protocol, Alice and Bob end up with a situation where they know that the other person did not choose a specific option, but they remain unsure between the other two. This "partial knowledge" is sufficient to create a shared secret. The researchers also showed that their method of using a single crystal to manage three different directions is a practical engineering solution that could be applied to other tasks in quantum technology, such as faster quantum computing or other forms of quantum sensing.

The team was careful to note that while their proof-of-concept worked well, there is still room for improvement. The speed of their current system is limited by the time it takes for the crystal to settle after changing its state, a phenomenon known as acoustic ringing. If this technical hurdle is overcome, the speed of generating keys could increase dramatically. Furthermore, the researchers pointed out that their method is particularly strong against a specific type of hacking attempt where an attacker tries to split a single photon into two. Because the protocol relies on the relationship between the bases rather than just the bits themselves, it offers a different kind of security that could be valuable in future networks.

Ultimately, this experiment bridges a gap between theoretical quantum mechanics and practical application. It shows that the strange, counterintuitive rules of the quantum world, where information can be incomplete yet still useful, can be harnessed to build real-world security systems. By proving that a secure key can be forged from partial information, the researchers have opened a new path for how we might think about privacy in a quantum future. The work stands as a clear demonstration that sometimes, knowing what something is not is just as powerful as knowing exactly what it is.

Technical Summary: Demonstration of a Partial Knowledge Quantum Key Distribution Protocol

Problem Statement
Traditional Quantum Key Distribution (QKD) protocols, such as BB84, generally operate under the assumption that communicating parties (Alice and Bob) acquire full information about each other's measured states after the sifting process. However, specific quantum scenarios, such as those involving the Hong-Ou-Mandel effect or the SARG04 protocol, yield only partial information about the prepared state. While the SARG04 protocol allows for partial information extraction by announcing bits rather than bases, it is limited to two dimensions and two bases, ultimately resulting in full shared information. There is a need to generalize this concept to higher dimensions and multiple bases where the sifting process inherently leaves parties with only partial knowledge of the other's raw key, yet still allows for the distillation of a secure mutual encryption key.

Methodology
The authors introduce and experimentally demonstrate the Bridge[d, q] protocol, a generalization of SARG04 to $d$ dimensions and $q$ bases. The specific experimental realization focuses on the Bridge[2, 3] protocol, utilizing a two-dimensional Hilbert space (qubits) and three mutually unbiased bases (MUBs): $B_x$ , $B_y$ , and $B_z$ .

Protocol Mechanics: In this scheme, Alice encodes a photon in a random state defined by a basis bit and a state bit. Bob measures in a random basis. During sifting, they retain only cases where their state bits differ ( $s_A \neq s_B$ ). In a noiseless scenario with three bases, this condition implies that their bases must also differ ( $b_A \neq b_B$ ). However, because there are three options, knowing that the bases are different does not reveal the specific basis used by the other party; it only eliminates one option. Consequently, Alice and Bob retain partial information (conditional entropy) about each other's bases. To distill a final key, they must perform information reconciliation to map these partially anti-correlated sequences into a shared bit string.
Experimental Setup: The experiment utilizes a weak coherent photon source (Ti:sapphire laser, 780 nm, 76 MHz) attenuated to a mean photon number of $\mu \approx 0.13$ $μ \approx 0.13$ .
- State Preparation: Alice's state bit ( $s_A$ ) is controlled by a "bit Pockels cell."
- Basis Selection: A novel configuration employs a single Pockels cell to switch between the three unbiased bases for both Alice and Bob. Photons traverse the cell, are reflected by a mirror, and pass through the cell again. By controlling the voltage on the electrodes, the cell performs specific rotations on the Bloch sphere.
- Rotation Logic: The setup utilizes the geometry of a trirectangular tetrahedron. By aligning the input polarization at an angle of $\theta_t \approx 54.7^\circ$ relative to the Pockels cell's rotation axis, and applying voltages corresponding to $2V_\pi/3$ , the system achieves rotations of $0$, $+2\pi/3$ , and $-2\pi/3$ . These rotations map the three unbiased bases onto one another.
- Timing: The system operates at a modulation frequency of 0.9 MHz to minimize acoustic ringing. The basis Pockels cell changes state between the forward and backward pass of the photon, ensuring that Alice and Bob effectively choose different bases for the same photon in specific instances required for the protocol.
- Detection: Photons are detected by Avalanche Photodiodes (APDs) after passing through a Polarizing Beam Splitter (PBS).

Key Contributions

Protocol Generalization: The paper defines the Bridge[d, q] protocol, extending the concept of partial knowledge QKD to arbitrary dimensions and bases.
Experimental Demonstration: The first experimental realization of the Bridge[2, 3] protocol, demonstrating that a secure key can be distilled even when Alice and Bob possess only partial information about each other's raw keys.
Hardware Innovation: The development of a method to switch between three mutually unbiased bases using a single Pockels cell via a double-pass reflection geometry. This reduces the number of active control elements compared to traditional multi-cell setups and is applicable to other quantum optics applications requiring fast polarization manipulation.

Results

State Fidelity: Quantum State Tomography (QST) performed on the prepared states yielded an average fidelity of 0.97 ± 0.02. The measured angle between the orthogonal axes was $88.6 \pm 1.8^\circ$ , close to the ideal $90^\circ$ .
Quantum Bit Error Rate (QBER): The experimental average QBER was measured at 2.8 ± 0.9%.
Security Analysis: Theoretical analysis indicates a critical QBER threshold of 5.75% for extracting a secure key. The experimental QBER is well below this threshold.
Key Rate:
- In a noiseless scenario, the secure key rate is theoretically $\log_2 3 - 1 \approx 0.585$ bits per sifted photon.
- Based on the experimental data, the conditional entropy between Alice and Bob is $H(A|B) = 1.14 \pm 0.03$ bits, and between Alice and Eve is $H(A|E) = 1.41 \pm 0.04$ bits.
- The resulting secure key rate is 0.26 ± 0.04 bits per sifted photon.
- Accounting for system losses and the specific timing constraints (one valid event every 84 laser pulses), the setup extracts approximately 200 ± 20 secure bits per second.

Significance
The paper claims that the Bridge protocol successfully demonstrates a QKD scenario where the communicating parties do not possess full information about each other's raw keys, yet a secure key can still be established. This validates the theoretical premise that partial information is sufficient for key distillation in specific quantum measurement contexts. Furthermore, the experimental configuration using a single Pockels cell for three-basis switching offers a practical advantage in reducing hardware complexity for protocols requiring fast, random basis selection. The authors note that while the current proof-of-concept is modest in rate, the approach is scalable and relevant for applications such as one-way quantum computation and the characterization of high-dimensional time-bin qudits.

Technical Summary: Demonstration of a Partial Knowledge Quantum Key Distribution Protocol

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