scholarly journals Communication Complexity of Statistical Distance

2018 ◽  
Vol 10 (1) ◽  
pp. 1-11
Author(s):  
Thomas Watson
Keyword(s):  
Communication Complexity ◽  
Statistical Distance

scholarly journals Secure k-ish Nearest Neighbors Classifier

2020 ◽  
Vol 2020 (3) ◽  
pp. 42-61
Author(s):  
Hayim Shaul ◽  
Dan Feldman ◽  
Daniela Rus
Keyword(s):  
Breast Tumor ◽  
Communication Complexity ◽  
State Of The Art ◽  
Homomorphic Encryption ◽  
Nearest Neighbors ◽  
Coin Toss ◽  
Running Time ◽  
Current State ◽  
Statistical Distance ◽  
Double Blinded

AbstractThe k-nearest neighbors (kNN) classifier predicts a class of a query, q, by taking the majority class of its k neighbors in an existing (already classified) database, S. In secure kNN, q and S are owned by two different parties and q is classified without sharing data. In this work we present a classifier based on kNN, that is more efficient to implement with homomorphic encryption (HE). The efficiency of our classifier comes from a relaxation we make to consider κ nearest neighbors for κ ≈k with probability that increases as the statistical distance between Gaussian and the distribution of the distances from q to S decreases. We call our classifier k-ish Nearest Neighbors (k-ish NN). For the implementation we introduce double-blinded coin-toss where the bias and output of the toss are encrypted. We use it to approximate the average and variance of the distances from q to S in a scalable circuit whose depth is independent of |S|. We believe these to be of independent interest. We implemented our classifier in an open source library based on HElib and tested it on a breast tumor database. Our classifier has accuracy and running time comparable to current state of the art (non-HE) MPC solution that have better running time but worse communication complexity. It also has communication complexity similar to naive HE implementation that have worse running time.

Nondeterministic and Randomized Boolean Hierarchies in Communication Complexity

2021 ◽  
Vol 30 (2) ◽  
Author(s):  
Toniann Pitassi ◽  
Morgan Shirley ◽  
Thomas Watson
Keyword(s):  
Communication Complexity

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

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.

scholarly journals Efficient experimental quantum fingerprinting with channel multiplexing and simultaneous detection

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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