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Frontiers in Optics

Realization of Communication Protocols with a Quantitative Quantum Communication Advantage

Juan Miguel Arrazola, Dave Touchette, Benjamin Lovitz, Markos Karasamanis, Norbert Lütkenhaus

Published Jan 1, 2016• 0 citations
Publisher

Abstract

Quantum Fingerprinting offers a exponential advantage over classical protocols in comparing two remote files by a referee in the simultaneous message passing protocol without shared randomness. We show how to realize this advantage using simple optical communication techniques.
DOI
10.1364/fio.2016.fth5f.3

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We study the power of quantum fingerprints in the simultaneous message passing (SMP) setting of communication complexity. Yao recently showed how to simulate, with exponential overhead, classical shared-randomness SMP protocols by means of quantum SMP protocols without shared randomness (Q∥Q^\parallelQ∥-protocols). Our first result is to extend Yao's simulation to the strongest possible model: every many-round quantum protocol with unlimited shared entanglement can be simulated, with exponential overhead, by Q∥Q^\parallelQ∥-protocols. We apply our technique to obtain an efficient Q∥Q^\parallelQ∥-protocol for a function which cannot be efficiently solved through more restricted simulations. Second, we tightly characterize the power of the quantum fingerprinting technique by making a connection to arrangements of homogeneous halfspaces with maximal margin. These arrangements have been well studied in computational learning theory, and we use some strong results obtained in this area to exhibit weaknesses of quantum fingerprinting. In particular, this implies that for almost all functions, quantum fingerprinting protocols are exponentially worse than classical deterministic SMP protocols.
We study the power of quantum fingerprints in the simultaneous message passing (SMP) setting of communication complexity. Yao recently showed how to simulate, with exponential overhead, classical shared-randomness SMP protocols by means of quantum SMP protocols without shared randomness (Qpar-protocols). Our first result is to extend Yao's simulation to the strongest possible model: every many-round quantum protocol with unlimited shared entanglement can be simulated, with exponential overhead, by Qpar-protocols. We apply our technique to obtain an efficient Qpar-protocol for a function which cannot be efficiently solved through more restricted simulations. Second, we tightly characterize the power of the quantum fingerprinting technique by making a connection to arrangements of homogeneous halfspaces with maximal margin. These arrangements have been well studied in computational learning theory, and we use some strong results obtained in this area to exhibit weaknesses of quantum fingerprinting. In particular, this implies that for almost all functions, quantum fingerprinting protocols are exponentially worse than classical deterministic SMP protocols
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.
Quantum fingerprinting (QF) promises exponential reduction of information transmission in executing communication complexity tasks. Practicality and quantum advantage of this novel protocol has been recently demonstrated using weak coherent pulses to carry the fingerprinting information. However, all coherent QF implementations rely upon a direct optical link to maintain coherence between the users, which does not comply with the protocol's rule that the users must not have any access to a shared randomness. To close this loophole, we propose, and experimentally demonstrate, a novel protocol based on asynchronous coincidence pairing from the interference result between coherent optical fields that are remotely and independently prepared. Over a length of 20 km telecom fiber, our QF setup has outperformed the best-known classical algorithm, for the first time without being susceptible to shared randomness. Our result paves the way toward practical applications of QF in communication complexity.
Classical fingerprinting associates with each string a shorter string (its fingerprint), such that any two distinct strings can be distinguished with small error by comparing their fingerprints alone. The fingerprints cannot be made exponentially smaller than the original strings unless the parties preparing the fingerprints have access to correlated random sources. We show that fingerprints consisting of quantum information can be made exponentially smaller than the original strings without any correlations or entanglement between the parties. This implies an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity.
When considering the complexity of communication protocols, the aim is to perform a certain task with the minimum amount of communication resources, such as time and transmitted information. The use of quantum states may lead to an exponential advantage in the use of such resources. Here, we are interested in the task of calculating the Euclidean distance between two vectors representing real data sets. It has been previously shown that it is possible to obtain an advantage for this task based on quantum fingerprinting. This protocol is defined in the simultaneous message passing model of communication complexity, where the two parties do not communicate with each other but send data to a third party, and exploits practical fingerprints generated using trains of coherent state pulses instead of highly entangled qubit states that are hard to generate for large input sizes needed to demonstrate an exponential advantage. We perform a proof-of-principle experimental demonstration of the Euclidean distance protocol using amplitude modulation techniques for encoding non-binary data sets and high-performance superconducting nanowire single-photon detectors required to increase the accessible input size. We show a quantum advantage in transmitted information surpassing the best classical protocol for an input size of 10810^8108, for diverse types of data sets, including those corresponding to real grayscale images, and with reasonable precision and error bounds. Our results highlight the potential of quantum communication complexity for use in a broad set of applications.