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arXiv:2002.10374 · Physical Review A

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

Li‐Yi Hsu, Ching–Yi Lai, You-Chia Chang, Chien-Ming Wu, Ray‐Kuang Lee

Published Aug 25, 2020• 8 citations
arXivHTMLPDF

Abstract

Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, resulting in 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\ifmmode \acute{c}\else \'{c}\fi{}. 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 and Bob whose detector clicks can access the other's full information of the $n$-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 an arbitrarily large (but finite) amount of information.

DOI
10.1103/physreva.102.022620

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Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, resulting in 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\ifmmode \acute{c}\else '{c}\fi{}. Suppose that Alice and Bob are distant from each other and each of them has an nnn-bit string. They are tasked to exchange the information of their local nnn-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 nnn-level MZ interferometers in our protocol, the one of Alice and Bob whose detector clicks can access the other's full information of the nnn-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 an arbitrarily large (but finite) amount of information.
In the beginning was the photon, and the photon was with information. Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, which then clicks. How much information can a photon carry? We study a bipartite asymmetric protocol as the extension of that proposed by Del Santo and Dakic. Suppose that Alice and Bob are distant from each other and each of them has an nnn-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 prove that, after the photon's travelling through a cascade of nnn-level MZ interferometers in our protocol, the one of Alice or Bob whose detector clicks can access the other's full information of nnn-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 infinite information as nnn goes infinite.
Nonclassical features of quantum systems have the potential to strengthen the way we currently exchange information. In this paper, we explore this enhancement on the most basic level of single particles. To be more precise, we compare how well multiparty information can be transmitted to a single receiver using just one classical or quantum particle. Our approach is based on a multiple-access communication model in which messages can be encoded into a single particle that is coherently distributed across multiple spatial modes. Theoretically, we derive lower bounds on the accessible information in the quantum setting that strictly separate it from the classical scenario. This separation is found whenever there is more than one sender, and also when there is just a single sender who has a shared phase reference with the receiver. When there is only one sender, the separation is impossible without a shared phase reference due to the famous Holevo's bound. Experimentally, we present a proof-of-principle demonstration of such quantum advantage in single-particle communication by implementing a multiport interferometer with messages being encoded along the different trajectories. Specifically, we consider a two-sender communication protocol built by a three-port optical interferometer. In this scenario, the rate sum achievable with a classical particle is upper bounded by one bit, while we experimentally observe a rate sum of $1.0152\ifmmode\pm\else\textpm\fi{}0.0034$ bits in the quantum setup.
We investigate in detail the assumptions under which secure quantum communications based on a single-photon interferometry scheme can be achieved. A Mach–Zehnder interferometer divided between two parties, with a message carried in the polarization of the photon and the superposition between the arms retained as a monitor for eavesdropping, is an appealing design because it dispenses with complementary bases, discards no photons due to sifting, and appears to offer direct communication without prior key exchange. Indeed, against every adversary who must act on a wavepacket at the moment it passes, the design behaves as intended. A single interaction with one arm is shown to be either informative or invisible but never both, while interception and re-sending is caught on half of the attacked rounds (twice as often as the corresponding attack on BB84 is caught). Moreover, we show that an adversary who detains a wavepacket incurs a delay bounded below by the vacuum traversal time of the link, which for a 50 km separation exceeds detector jitter by six orders of magnitude. However, an adversary equipped with a quantum memory may interact unitarily with the first wavepacket, retain the ancilla without measuring it, and interact with the second when it arrives, recovering the message with certainty while leaving the interference, arrival times, and delivered polarization exactly as they would have been. Notably, this requires neither simultaneous access to the two arms nor any joint operation upon them. The reason is that the message occupies a variable that each wavepacket carries in full, encoded in a public basis, so that a non-demolition measurement of it acts as the identity on the encoded alphabet; moving the message into the relative phase repairs the scheme. We prove that no sequential attack then yields any information whatsoever, and the causal structure of the link (an irrelevance for a locally encoded message) becomes exactly the resource that makes the proof available. We give the resulting security claim, its conditions, and its costs.
One of the standard communication complexity problems is deciding whether bit strings held by two separate parties Alice (A) and Bob (B) are equal or different. In the simultaneous message passing model, A and B send certain information to a Referee, who makes the decision. The overall goal is to minimize the amount of communication involved while not exceeding desired error probability. This is achieved by sending only fingerprints of the original n-bit strings. In the best classical protocols, these scale as O(√n) if A and B have no access to shared randomness [1]. The recently proposed [2] and demonstrated quantum fingerprinting [3], exploiting phase-modulated weak coherent pulses, provides O(log2n) scaling in the number of used qubits, but needs phase stability between A and B. Here we introduce and analyse a quantum fingerprinting protocol based on two-photon interference which does require a shared phase reference and works in scenarios when the global phase of transmitted signals becomes completely random. Interestingly, the performance of this protocol, quantified in terms of the Chernoff information [4], is enhanced through the use of non-classical single-photon states, even in the regime of high transmission loss.