The Complexity of Classical and Quantum Branching Programs: A Communication Complexity Approach

AbstractQuantum correlations, in particular those, which enable to violate a Bell inequality, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles N. In case of Dicke states, we show that persistency can reach 0.482N, significantly more than reported in previous studies.

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Efficient experimental quantum fingerprinting with channel multiplexing and simultaneous detection

Nature Communications ◽

10.1038/s41467-021-24745-x ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Xiaoqing Zhong ◽

Feihu Xu ◽

Hoi-Kwong Lo ◽

Li Qian

Keyword(s):

Communication Complexity ◽

Single Photon ◽

Simultaneous Detection ◽

Minimum Amount ◽

Photon Detectors ◽

Communication Time ◽

Quantum Communication Complexity ◽

Detection Of Signals ◽

Coherent Quantum ◽

Quantum Fingerprinting

AbstractQuantum communication complexity explores the minimum amount of communication required to achieve certain tasks using quantum states. One representative example is quantum fingerprinting, in which the minimum amount of communication could be exponentially smaller than the classical fingerprinting. Here, we propose a quantum fingerprinting protocol where coherent states and channel multiplexing are used, with simultaneous detection of signals carried by multiple channels. Compared with an existing coherent quantum fingerprinting protocol, our protocol could consistently reduce communication time and the amount of communication by orders of magnitude by increasing the number of channels. Our proposed protocol can even beat the classical limit without using superconducting-nanowire single photon detectors. We also report a proof-of-concept experimental demonstration with six wavelength channels to validate the advantage of our protocol in the amount of communication. The experimental results clearly prove that our protocol not only surpasses the best-known classical protocol, but also remarkably outperforms the existing coherent quantum fingerprinting protocol.

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