Beating the channel capacity limit for linear photonic superdense coding

Abstract: Dense coding is arguably the protocol that launched the field of quantum communication. Today, however, more than a decade after its initial experimental realization, the channel capacity remains fundamentally limited as conceived for photons using linear elements. Bob can only send to Alice three of four potential messages owing to the impossibility of carrying out the deterministic discrimination of all four Bell states with linear optics, reducing the attainable channel capacity from 2 to log_2 3 \approx 1.585 bits. However, entanglement in an extra degree of freedom enables the complete and deterministic discrimination of all Bell states. Using pairs of photons simultaneously entangled in spin and orbital angular momentum, we demonstrate the quantum advantage of the ancillary entanglement. In particular, we describe a dense-coding experiment with the largest reported channel capacity and, to our knowledge, the first to break the conventional linear-optics threshold. Our encoding is suited for quantum communication without alignment and satellite communication.

• The paper demonstrates a novel application of hyperentanglement to achieve deterministic Bell-state discrimination in photonic dense coding.
• It introduces a custom interferometric setup that boosts channel capacity to 1.630(6) bits with over 94% detection accuracy.
• The findings advance quantum communication by overcoming linear optics limits, paving the way for secure, high-capacity networks.

Beating the Channel Capacity Limit for Linear Photonic Superdense Coding

This paper tackles a fundamental limitation in the field of quantum communication by exploring the potential of exceeding channel capacity in linear photonic superdense coding. The study extends the dense coding protocol, a cornerstone in quantum communication, to surpass barriers imposed by traditional linear optical systems. The primary innovation in this work is the use of hyperentanglement to achieve complete deterministic discrimination of all four Bell states, an achievement not possible with standard linear optics alone.

Theoretical Background and Methodology

Dense coding conventionally allows the transfer of two classical bits through the transmission of a single qubit when each party holds part of a maximally entangled pair. However, the limitation arises because of the inability to deterministically distinguish all four Bell states using only linear optics, resulting in a reduction of the channel capacity from 2 bits to approximately $\log_2 3 \approx 1.585$ bits. Probabilistic approaches exist but are capped by a 50% success rate, thus offering no significant advantage.

This paper leverages hyperentanglement by entangling the photon pairs in both spin and orbital angular momentum (OAM), thereby providing an extra degree of freedom that facilitates full Bell state analysis with linear optical elements—a task commonly requiring nonlinear optics. The hyperentangled states are manipulated and analyzed through a thoroughly designed experiment setup including a novel interferometric apparatus enabling deterministic Bell-state analysis.

Experimental Implementation and Outcomes

The experimental framework consists of three main stages: a quantum hyperentanglement source, encoding elements manipulated by select unitary operations, and a Bell-state analyzer able to deterministically differentiate among the four encoded states. The hyperentanglement source produces pairs of photons entangled simultaneously in polarization and OAM.

Results demonstrated a significant channel capacity of 1.630(6) bits, surpassing the conventional linear-optics threshold. The system exhibited a high success rate with average conditional detection probabilities for all encoded states exceeding 94%. The customized interferometric setup, alongside precise calibration and detection techniques, contributed to this advanced capacity and reliable discrimination fidelity.

Implications and Future Directions

The theoretical implications of surpassing the channel capacity limit using hyperentangled photons extend the understanding of quantum communication paradigms. Practically, this enhancement suggests potential applications in secure communications, particularly in contexts where high-fidelity and high capacity are critical. The methodology points towards feasible implementations in high-dimensional quantum systems and robust quantum networks.

Future studies might explore optimizing the number of entangled degrees of freedom to increase channel capacity further. There is a potential to extend this approach by investigating other types of hyperentanglement or employing advanced photon detection techniques, allowing for complex quantum systems to be effectively utilized in dense coding.

Furthermore, considering the implementation efforts required for practical deployment, explorations into reducing the decoherence particularly affecting OAM states during atmospheric transmission are crucial. This direction aligns with advancing communication technologies such as satellite-based quantum communications where conditions for OAM transmission stability may be more favorable.

In conclusion, this work establishes a practical step forward in overcoming a longstanding limitation in quantum communication, setting a benchmark for future innovations in superdense coding and broader quantum information science.