Single-Photon Advantage in Quantum Cryptography Beyond QKD

TL;DR

This work demonstrates a quantum advantage for a cryptographic primitive beyond QKD by experimentally implementing quantum strong coin flipping (QSCF) with a deterministic single-photon source based on a quantum dot in a high-Purcell microcavity. Dynamic random polarization-state encoding at $R_0=80\ \mathrm{MHz}$ yields a low QBER of $e\approx 2.8\%$ and enables back-to-back QSCF at ~1 kbit/s, with cheating probabilities below the corresponding classical bound. Comparisons show a clear single-photon advantage over faint laser pulses (WCP) and, in simulations and experiments, a quantum advantage relative to the classical protocol up to about $1.6$ percentage points, robust to modest channel loss (tested up to 3 dB) and scalable toward longer distances with telecom-wavelength operation. These results illustrate practical pathways for complex cryptographic tasks in a future quantum internet using on-demand, sub-Poissonian light sources.

Abstract

Quantum key distribution (QKD) can be used to establish a secret key between trusted parties. Many practical use-cases in communication networks, however, involve parties who do not trust each other. A fundamental cryptographic building block for such distrustful scenarios is quantum coin flipping, which has been investigated only in few experimental studies to date, all of which used probabilistic quantum light sources imposing fundamental limitations. Here, we experimentally implement a quantum strong coin flipping protocol using single-photon states and demonstrate a quantum advantage compared to both classical realizations and implementations using faint laser pulses. We achieve this by employing a state-of-the-art deterministic quantum dot light source in combination with fast, random polarization-state encoding enabling sufficiently low quantum bit error ratio. By demonstrating a single-photon quantum advantage in a cryptographic primitive beyond QKD, our work represents a major advance towards the implementation of complex cryptographic tasks in a future quantum internet.

Figures (13)

• Figure 1: Schematic of the QSCF protocol implemented in this work: 1. Alice randomly prepares pulse number $i$ of the $K$-long sequence in one out of four pre-optimized coin flipping states $\ket{\phi_{\alpha_i,c_i}}$ and sends them to Bob. The states are rotated relative to the standard BB84 states (dashed gray lines). 2. Bob projects the received pulses randomly into one of the same four states and calls the first detected event $j$. 3. Bob now sends a random number $b_j$ and the pulse number $j$ to Alice. 4. Alice returns her initial bit $c_j$ and basis $\alpha_j$ for that pulse. 5. If Bob measures a different state for the same basis, he aborts. 6. If the protocol is not aborted the coin flip result is $c_j \bigoplus b_j$.
• Figure 2: Cheating probabilities for the QSCF protocol: (a) Plotted as a function of the number of rounds $K$ per coin flip for implementations using a single-photon source (SPS, green), weak coherent pulses (WCP, blue), and an equivalent classical implementation (Class., black) assuming $\mu = 0.0013$. An ideal single photon source without multi-photon pulses is shown as a reference (dashed green line). (b) and (c) Reduction of cheating probability compared with classical protocol as a function of $K$ and $\mu$ achievable in the QSCF protocol implemented with an attenuated laser and a sub-Poissonian light source ($g^{(2)}(0) = 0.03$), respectively. White circles mark the operating point of our experiment.
• Figure 3: (a) Experimental setup for QSCF: Alice generates single photons using a quantum dot microcavity and randomly switches their polarization state between the four protocol states using a fiber-coupled electro-optical modulator (EOM) controlled by a self-built arbitrary waveform generator (AWG). The polarization-encoded qubits propagate through a quantum channel and are detected in a 4-state polarization analyzer with passive bases choice on Bob's side. (BS: beam splitter, LP: linear polarizer, PBS: polarizing BS, DAC: digital-to-analog converter, FPGA: field-programmable-gate-array, Amp: Amplifier, SM: single-mode). (b) Emission spectrum of the single-photon source and (c) Hanbury-Brown and Twiss experiment confirming the single-photon nature of the spectrally filtered emission from (b) (red shaded area). (d) Measurement of the photon number coherence using phase-resolved two-photon interference experiments under p-shell (dark lines) and strict resonant (light lines) excitation. As QSCF requires vanishing photon number coherence, quasi-resonant excitation was chosen for the protocol implementation in this work.
• Figure 4: Creating the polarization states: (a) The four states used in the QSCF protocol are defined by the parameter $a=0.9$ and marked on the Poincaré sphere. (b) Exemplary sequence showing random voltage-level switching as used in our protocol implementation to modulate the EOM for dynamic polarization qubit encoding. Full horizontal lines indicate the four target states of the QSCF protocol. Dashed lines indicate the states typically used in BB84 QKD $\{H,D,V,A\}$ serving as a reference. Note that we employed an advanced coding scheme requiring an effectively doubled clock-rate of 160 MHz inside the control electronics, preventing voltage level drifts as described in the main text. The gray shaded window indicates the 12.5$\,$ns wide period defined by the 80 MHz laser clock-rate, where the polarization encoding of the photon is performed during the first 6.25 ns of the window.
• Figure 5: Analyzing single photon states: (a) Time traces of single-photon pulses under dynamic random switching between the four QSCF states as detected on Bob's side after projection into the four different target channels (top to bottom). (b) Zoom-in from (a) with shaded regions indicating the prepared state by the color coding. (c) Integrating over all coin flip realizations and comparing prepared and detected states yields input-output matrices from which the QBER can be computed. Introducing additional loss in the quantum channel, the QBER increases and the received statistics start to differ from the expected case for $a=0.9$ (left panel).