Carrying an arbitrarily large amount of information using a single quantum particle

Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, resulting a click. How much information can a photon carry? We study a bipartite asymmetric "two-way signaling" protocol as an extension of that proposed by Del Santo and Daki\'{c}. Suppose that Alice and Bob are distant from each other and each of them has an $n$-bit string. They are tasked to exchange the information of their local n-bit strings with each other, using only a single photon during the communication. It has been shown that the superposition of different spatial locations in a Mach-Zehnder (MZ) interferometer enables bipartite local encodings. We show that, after the travel of a photon through a cascade of $n$-level MZ interferometers in our protocol, the one of Alice or Bob whose detector clicks can access the other's full information of $n$-bit string, while the other can gain one-bit of information. That is, the wave-particle duality makes two-way signaling possible, and a single photon can carry arbitrarily large (but finite) information.