Maximal $α$-Leakage for Quantum Privacy Mechanisms

• URL: http://arxiv.org/abs/2403.14450v1
• Date: Thu, 21 Mar 2024 14:58:07 GMT
• Title: Maximal $α$-Leakage for Quantum Privacy Mechanisms
• Abstract summary: We first show that an adversary's maximal expected $alpha$-gain is characterized by measured conditional R'enyi entropy. We prove that the $alpha$-leakage and maximal $alpha$-leakage for a quantum privacy mechanism are determined by measured Arimoto information and measured R'enyi capacity.
• Score: 8.259231344795781
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, maximal $\alpha$-leakage is introduced to quantify how much a quantum adversary can learn about any sensitive information of data upon observing its disturbed version via a quantum privacy mechanism. We first show that an adversary's maximal expected $\alpha$-gain using optimal measurement is characterized by measured conditional R\'enyi entropy. This can be viewed as a parametric generalization of K\"onig et al.'s famous guessing probability formula [IEEE Trans. Inf. Theory, 55(9), 2009]. Then, we prove that the $\alpha$-leakage and maximal $\alpha$-leakage for a quantum privacy mechanism are determined by measured Arimoto information and measured R\'enyi capacity, respectively. Various properties of maximal $\alpha$-leakage, such as data processing inequality and composition property are established as well. Moreover, we show that regularized $\alpha$-leakage and regularized maximal $\alpha$-leakage for identical and independent quantum privacy mechanisms coincide with $\alpha$-tilted sandwiched R\'enyi information and sandwiched R\'enyi capacity, respectively.

Related papers

• Hiai--Petz Skew Informations and Sharp Uncertainty Relations for a Single Observable [0.0]
  We study intrinsic quantum uncertainty associated with a single observable from the viewpoint of skew information.<n>By relaxing ordinary additivity we introduce a class of Hiai--Petz nonadditive skew informations.<n>Our main quantitative result is a sharp single-observable uncertainty relation for the full Hiai--Petz class.
  arXiv  Detail & Related papers  (2026-09-12T10:45:46Z)
• Optimal Unconstrained Self-Distillation in Ridge Regression: Strict Improvements, Precise Asymptotics, and One-Shot Tuning [61.07540493350384]
  Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth and the teacher's own predictions.<n>We show that for any prediction risk, the optimally mixed student improves upon the ridge teacher for every regularization level.<n>We propose a consistent one-shot tuning method to estimate $star$ without grid search, sample splitting, or refitting.
  arXiv  Detail & Related papers  (2026-02-19T17:21:15Z)
• Locally Gentle State Certification for High Dimensional Quantum Systems [1.1470070927586014]
  Standard approaches to quantum statistical inference rely on measurements that induce a collapse of the wave function.<n>We investigate the limits of emphlocally-gentle quantum state certification, where the learning algorithm is constrained to perturb the state by at most $$ in trace norm.<n>Our results clarify the trade-off between information extraction and state disturbance, and highlight deep connections between physical measurement constraints and privacy mechanisms in quantum learning.
  arXiv  Detail & Related papers  (2026-02-04T13:41:11Z)
• When the Weak Becomes Strong: Effective Observables via Time-Symmetric Quantum Selection [0.0]
  We investigate the sequential composition of weak values in the framework of time-symmetric quantum mechanics.<n>We show that the product of these two weak values corresponds to the normalized expectation value of a strong, state-conditioned observable.<n>We illustrate practical applications in quantum information, including state-specific error witnessing in quantum computing.
  arXiv  Detail & Related papers  (2025-07-13T17:25:45Z)
• Rényi divergence-based uniformity guarantees for $k$-universal hash functions [59.90381090395222]
  Universal hash functions map the output of a source to random strings over a finite alphabet. We show that it is possible to distill random bits that are nearly uniform, as measured by min-entropy.
  arXiv  Detail & Related papers  (2024-10-21T19:37:35Z)
• Deterministic identification over channels with finite output: a dimensional perspective on superlinear rates [53.66705737169404]
  We consider the problem in its generality for memoryless channels with finite output, but arbitrary input alphabets. Our main findings are that the maximum number of messages thus identifiable scales super-exponentially as $2R,nlog n$ with the block length $n$. Results are shown to generalise directly to classical-quantum channels with finite-dimensional output quantum system.
  arXiv  Detail & Related papers  (2024-02-14T11:59:30Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Approximation Algorithms for Quantum Max-$d$-Cut [42.248442410060946]
  The Quantum Max-$d$-Cut problem involves finding a quantum state that maximizes the expected energy associated with the projector onto the antisymmetric subspace of two, $d$-dimensional qudits over all local interactions. We develop an algorithm that finds product-state solutions of mixed states with bounded purity that achieve non-trivial performance guarantees.
  arXiv  Detail & Related papers  (2023-09-19T22:53:17Z)
• Maximal Information Leakage from Quantum Encoding of Classical Data [9.244521717083696]
  An adversary can access a single copy of the state of a quantum system that encodes some classical data. The resulting measure of information leakage is the multiplicative increase of the probability of correctly guessing any function of the classical data.
  arXiv  Detail & Related papers  (2023-07-24T05:16:02Z)
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees [0.0]
  We provide theoretical guarantees for efficient learning of quantum many-body states and their properties, with model-independent applications. Our results provide theoretical guarantees for efficient learning of quantum many-body states and their properties, with model-independent applications.
  arXiv  Detail & Related papers  (2023-04-10T02:22:36Z)
• Large $N$ Matrix Quantum Mechanics as a Quantum Memory [7.667124030138028]
  We study the possibility of building a quantum memory that is robust to thermal noise using large $N$ matrix quantum mechanics models. We find that the effects of gauging can be mimicked using an energy penalty to give a similar result for the memory time.
  arXiv  Detail & Related papers  (2022-11-15T19:01:04Z)
• High Probability Bounds for a Class of Nonconvex Algorithms with AdaGrad Stepsize [55.0090961425708]
  We propose a new, simplified high probability analysis of AdaGrad for smooth, non- probability problems. We present our analysis in a modular way and obtain a complementary $mathcal O (1 / TT)$ convergence rate in the deterministic setting. To the best of our knowledge, this is the first high probability for AdaGrad with a truly adaptive scheme, i.e., completely oblivious to the knowledge of smoothness.
  arXiv  Detail & Related papers  (2022-04-06T13:50:33Z)
• Optimal Second-Order Rates for Quantum Soft Covering and Privacy Amplification [19.624719072006936]
  We study quantum soft covering and privacy amplification against quantum side information. For both tasks, we use trace distance to measure the closeness between the processed state and the ideal target state. Our results extend to the moderate deviation regime, which are the optimal rates when the trace distances vanish at sub-exponential speed.
  arXiv  Detail & Related papers  (2022-02-23T16:02:31Z)
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification [56.61325554836984]
  The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
  arXiv  Detail & Related papers  (2021-11-01T16:35:41Z)
• Nonlocal realism tests and quantum state tomography in Sagnac-based type-II polarization-entanglement SPDC-source [0.0]
  We have experimentally created a robust, ultrabright and phase-stable polarization-entangled state close to maximally entangled Bell-state. We have obtained very reliable and very strong Bell violation as $ S=2.78 pm 0.01 $ with high brightness. The Sagnac configuration provides bidirectional crystal pumping yields to high-rate entanglement source.
  arXiv  Detail & Related papers  (2020-12-04T17:12:17Z)
• Quantum Differentially Private Sparse Regression Learning [132.1981461292324]
  We devise an efficient quantum differentially private (QDP) Lasso estimator to solve sparse regression tasks. Last, we exhibit that the QDP Lasso attains a near-optimal utility bound $tildeO(N-2/3)$ with privacy guarantees.
  arXiv  Detail & Related papers  (2020-07-23T10:50:42Z)

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.