Beating the channel capacity limit for superdense coding with entangled ququarts

Abstract

Quantum superdense coding protocols enhance channel capacity by using shared quantum entanglement between two users. The channel capacity can be as high as 2 when one uses entangled qubits. However, this limit can be surpassed by using high-dimensional entanglement. We report an experiment that exceeds the limit using high-quality entangled ququarts with fidelities up to 0.98, demonstrating a channel capacity of 2.09 ± 0.01. The measured channel capacity is also higher than that obtained when transmitting only one ququart. We use the setup to transmit a five-color image with a fidelity of 0.952. Our experiment shows the great advantage of high-dimensional entanglement and will stimulate research on high-dimensional quantum information processes.

Fig. 1. Experimental setup.

A continuous-wave violet laser (power, 4 mW; wavelength, 404 nm) is focused by two lenses, and the waist radius is approximately 0.25 mm. Then, the light beam is separated into two paths by a BD. These two beams are injected into a Sagnac interferometer to pump a type II cut periodically poled potassium titanyl phosphate (ppKTP) crystal (1 mm × 7 mm × 10 mm) and generate two-photon polarization entanglement $(|\mathit{H}\rangle |\mathit{H}\rangle +|\mathit{V}\rangle |\mathit{V}\rangle )/\sqrt{2}$ in each path (33). The ppKTP is temperature-controlled by a homemade temperature controller, and the temperature stability is K to ensure the phase stability between the two paths. Then, we encode horizontally polarized (H) photons in path a1 (a3) as |0〉, vertically polarized (V) photons in path a1 (a3) as |1〉, H photons in path a2 (a4) as |2〉, and V photons in path a2 (a4) as |3〉 and carefully adjust the relative phase between the two paths; the state is prepared in a four-dimensional maximally entangled two-photon state Ψ₁₁ = (|00〉 + |11〉 + |22〉 + |33〉)/2. Finally, Alice encodes her information using four computer-controlled LCs and sends her photon to Bob. Bob performs a measurement on the two photons and decodes the information that Alice encoded (details can be found in the Supplementary Materials). PBS, polarizing beam splitter; HWP, half-wave plate.

Fig. 2. Measured probabilities.

Alice sends the five four-dimensional Bell states to Bob, and Bob performs a measurement on the two photons and obtains the probabilities for each state. In our experiment, the photon-pair count rate is 1000/s, and the integration time is 20 s for each input state. Error bars are due to the statistical error.

Fig. 3. Transmit a real five-color image using encoded information.

Red spots are encoded to Ψ₁₁, yellow spots are encoded to Ψ₁₂, blue spots are encoded to Ψ_13s, green spots are encoded to Ψ₁₄, and white spots are encoded to Ψ₂₃. (A) Original five-color 53 × 188 pixel image. (B) Image received using SDC. The calculated fidelity is 0.952.

Fig. 4. Realization of a single-photon operation on Alice’s side.

The optical axes of the LCs are set at different angles, as shown in the figure. By applying different voltages, the LCs will introduce different phases between the fast axis and the slow axis.