Biased Random Access Codes

• URL: http://arxiv.org/abs/2302.08494v3
• Date: Thu, 12 Oct 2023 14:08:23 GMT
• Title: Biased Random Access Codes
• Authors: Gabriel Pereira Alves, Nicolas Gigena, J\k{e}drzej Kaniewski
• Abstract summary: A random access code (RAC) is a communication task in which the sender encodes a random message into a shorter one to be decoded by the receiver. We present algorithms that allow a numerical evaluation of the optimal performance over both classical and quantum strategies.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A random access code (RAC) is a communication task in which the sender encodes a random message into a shorter one to be decoded by the receiver so that a randomly chosen character of the original message is recovered with some probability. Both the message and the character to be recovered are assumed to be uniformly distributed. In this paper, we extend this protocol by allowing more general distributions of these inputs, which alters the encoding and decoding strategies optimizing the protocol performance, with either classical or quantum resources. We approach the problem of optimizing the performance of these biased RACs with both numerical and analytical tools. On the numerical front, we present algorithms that allow a numerical evaluation of the optimal performance over both classical and quantum strategies and provide a Python package designed to implement them, called RAC-tools. We then use this numerical tool to investigate single-parameter families of biased RACs in the $n^2 \mapsto 1$ and $2^d \mapsto 1$ scenarios. For RACs in the $n^2 \mapsto 1$ scenario, we derive a general upper bound for the cases in which the inputs are not correlated, which coincides with the quantum value for $n=2$ and, in some cases for $n=3$. Moreover, it is shown that attaining this upper bound self-tests pairs or triples of rank-1 projective measurements, respectively. An analogous upper bound is derived for the value of RACs in the $2^d \mapsto 1$ scenario, which is shown to be always attainable using mutually unbiased measurements if the distribution of input strings is unbiased.

Related papers

• Relative-Translation Invariant Wasserstein Distance [82.6068808353647]
  We introduce a new family of distances, relative-translation invariant Wasserstein distances ($RW_p$) We show that $RW_p distances are also real distance metrics defined on the quotient set $mathcalP_p(mathbbRn)/sim$ invariant to distribution translations.
  arXiv  Detail & Related papers  (2024-09-04T03:41:44Z)
• Some Notes on the Sample Complexity of Approximate Channel Simulation [2.4554686192257424]
  Channel simulation algorithms can efficiently encode random samples from a prescribed target distribution $Q$ and find applications in machine learning-based lossy data compression. This paper considers approximate schemes with a fixed runtime instead. We exploit global-bound, depth-limited A* coding to ensure $mathrmTV[Q Vert P] leq epsilon$ and maintain optimal coding performance with a sample complexity of only $expbig((D_KL[Q Vert P] + o(1)) big/ epsilonbig
  arXiv  Detail & Related papers  (2024-05-07T14:44:41Z)
• Linear-time Minimum Bayes Risk Decoding with Reference Aggregation [52.1701152610258]
  Minimum Bayes Risk (MBR) decoding is a text generation technique that has been shown to improve the quality of machine translations. It requires the pairwise calculation of a utility metric, which has quadratic complexity. We propose to approximate pairwise metric scores with scores calculated against aggregated reference representations.
  arXiv  Detail & Related papers  (2024-02-06T18:59:30Z)
• SpecTr: Fast Speculative Decoding via Optimal Transport [30.18181671899423]
  We develop a new autoregressive sampling algorithm called $textitSpecTr$, which provides speedup in decoding while ensuring that there is no quality degradation in the decoded output. We experimentally demonstrate that for state-of-the-art large language models, the proposed approach achieves a wall clock speedup of 2.13X, a further 1.37X speedup over speculative decoding on standard benchmarks.
  arXiv  Detail & Related papers  (2023-10-23T17:47:34Z)
• Replicable Clustering [57.19013971737493]
  We propose algorithms for the statistical $k$-medians, statistical $k$-means, and statistical $k$-centers problems by utilizing approximation routines for their counterparts in a black-box manner. We also provide experiments on synthetic distributions in 2D using the $k$-means++ implementation from sklearn as a black-box that validate our theoretical results.
  arXiv  Detail & Related papers  (2023-02-20T23:29:43Z)
• Rapid Person Re-Identification via Sub-space Consistency Regularization [51.76876061721556]
  Person Re-Identification (ReID) matches pedestrians across disjoint cameras. Existing ReID methods adopting real-value feature descriptors have achieved high accuracy, but they are low in efficiency due to the slow Euclidean distance computation. We propose a novel Sub-space Consistency Regularization (SCR) algorithm that can speed up the ReID procedure by 0.25$ times.
  arXiv  Detail & Related papers  (2022-07-13T02:44:05Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• PAC Mode Estimation using PPR Martingale Confidence Sequences [5.623190096715942]
  We consider the problem of correctly identifying the mode of a discrete distribution $mathcalP$ with sufficiently high probability. We propose a generalisation to mode estimation, in which $mathcalP$ may take $K geq 2$ values. Our resulting stopping rule, denoted PPR-ME, is optimal in its sample complexity up to a logarithmic factor.
  arXiv  Detail & Related papers  (2021-09-10T18:11:38Z)
• List-Decodable Mean Estimation in Nearly-PCA Time [50.79691056481693]
  We study the fundamental task of list-decodable mean estimation in high dimensions. Our algorithm runs in time $widetildeO(ndk)$ for all $k = O(sqrtd) cup Omega(d)$, where $n$ is the size of the dataset. A variant of our algorithm has runtime $widetildeO(ndk)$ for all $k$, at the expense of an $O(sqrtlog k)$ factor in the recovery guarantee
  arXiv  Detail & Related papers  (2020-11-19T17:21:37Z)
• Quantum Random Access Codes for Boolean Functions [0.05076419064097732]
  We study and give protocols for $f$-random access codes with classical ($f$-RAC) and quantum ($f$-QRAC) encoding. The success probability of our protocols is characterized by the emphnoise stability of the Boolean function $f$.
  arXiv  Detail & Related papers  (2020-11-12T17:48:37Z)
• Towards Tight Communication Lower Bounds for Distributed Optimisation [30.134447658488057]
  We consider a standard distributed optimisation setting where $N$ machines aim to jointly minimise the sum of the functions $sum_i = 1N f_i (x)$. Our main result provides the first fully unconditional bounds on total number of bits which need to be sent and received by the $N$ machines. We show that $Omega( Nd log d / Nvarepsilon)$ total bits need to be communicated between the machines to find an additive $epsilon$-approximation to the minimum of $sum_i = 1N
  arXiv  Detail & Related papers  (2020-10-16T08:10:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.