Geometrical realization of set systems and probabilistic communication complexity

We consider the fair division of indivisible items using the maximin shares measure. Recent work on the topic has focused on extending results beyond the class of additive valuation functions. In this spirit, we study the case where the items form a hereditary set system. We present a simple algorithm that allocates each agent a bundle of items whose value is at least 0.3666 times the maximin share of the agent. This improves upon the current best known guarantee of 0.2 due to Ghodsi et al. The analysis of the algorithm is almost tight; we present an instance where the algorithm provides a guarantee of at most 0.3738. We also show that the algorithm can be implemented in polynomial time given a valuation oracle for each agent.

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Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures

Scientific Reports ◽

10.1038/s41598-021-93786-5 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Marcin Wieśniak

Keyword(s):

Communication Complexity ◽

Quantum Communication ◽

Bell Inequality ◽

Bell Inequalities ◽

Quantum Correlations ◽

Complexity Reduction ◽

Main Difficulty ◽

Quantum Communication Complexity ◽

Number Of Particles ◽

Dicke States

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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Simple communication complexity separation from quantum state antidistinguishability

Physical Review Research ◽

10.1103/physrevresearch.2.013326 ◽

2020 ◽

Vol 2 (1) ◽

Cited By ~ 1

Author(s):

Vojtěch Havlíček ◽

Jonathan Barrett

Keyword(s):

Quantum State ◽

Communication Complexity

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