Almost-iid information theory

• URL: http://arxiv.org/abs/2603.15792v1
• Date: Mon, 16 Mar 2026 18:21:47 GMT
• Title: Almost-iid information theory
• Abstract summary: Information-theoretic techniques are based on the assumption that resources are well characterized by independent and identically distributed (iid) states.<n> Operationally motivated assumptions still imply, via de Finettis theorems, that the resources are described by almost-iid states.<n>Here we prove that the conditional symmetry of almost-iid states coincides with that of iid states.
• Score: 3.8870795921263714
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Information-theoretic techniques are based on the assumption that resources are well characterized by independent and identically distributed (iid) states. This assumption cannot be justified operationally, since, for example, correlations between subsequent systems emitted by a source cannot be detected by any practical tomographic protocol. Operationally motivated symmetry assumptions still imply, via de Finetti theorems, that the resources are described by almost-iid states. This raises the question: Are almost-iid resources as effective as perfect iid resources for information-processing tasks? Here we address this question and prove that the conditional entropy of almost-iid states asymptotically coincides with that of iid states. As an application, this implies that squashed entanglement is robust for almost-iid states, asymptotically matching its value on iid states.

Related papers

• Causal-Order Identification of Memoryless Sequential Quantum Processes from Restricted Projective Data [45.85698554568285]
  We find necessary and sufficient conditions for deciding when an observed distribution is compatible with a memoryless sequential quantum process in a fixed direction.<n>We then specialize to the two-qubit Pauli setting, where the problem remains non-tomographic but becomes explicitly tractable.
  arXiv  Detail & Related papers  (2026-05-06T07:16:29Z)
• Resource theory of asymmetric distinguishability with partial information [2.0094233004333124]
  Worst-case quantum divergence is a key measure in quantum information.<n>We show that divergences can be understood from the perspective of the resource theory of asymmetric distinguishability.<n>We extend this framework to settings with partial information.
  arXiv  Detail & Related papers  (2025-10-02T14:35:09Z)
• A Sample Efficient Conditional Independence Test in the Presence of Discretization [54.047334792855345]
  Conditional Independence (CI) tests directly to discretized data can lead to incorrect conclusions.<n>Recent advancements have sought to infer the correct CI relationship between the latent variables through binarizing observed data.<n>Motivated by this, this paper introduces a sample-efficient CI test that does not rely on the binarization process.
  arXiv  Detail & Related papers  (2025-06-10T12:41:26Z)
• General detectability measure [45.85698554568285]
  Distinguishing resource states from resource-free states is a fundamental task in quantum information.<n>We derived the optimal exponential decay rate of the failure probability for detecting a given $n$-tensor product state.
  arXiv  Detail & Related papers  (2025-01-16T05:39:22Z)
• Investigating Pure State Uniqueness in Tomography via Optimization [4.396311564396993]
  Quantum state (QST) is crucial for understanding and characterizing quantum systems through measurement data.<n>Traditional QST methods face scalability challenges, requiring $mathcalO(d2) measurements for a generaldimensionald state.<n>We develop a unified framework based on the Augmented Lagrangian Method (ALM) to address these issues.
  arXiv  Detail & Related papers  (2024-12-31T07:57:03Z)
• All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources [0.0]
  We show that all non-Gaussian states can provide an advantage in some channel discrimination task, even those that are simply mixtures of Gaussian states.<n>We apply our results to a key case study in variable quantum information: the resource theory of non-Gaussianity.
  arXiv  Detail & Related papers  (2024-12-17T15:32:59Z)
• Prototype-based Aleatoric Uncertainty Quantification for Cross-modal Retrieval [139.21955930418815]
  Cross-modal Retrieval methods build similarity relations between vision and language modalities by jointly learning a common representation space. However, the predictions are often unreliable due to the Aleatoric uncertainty, which is induced by low-quality data, e.g., corrupt images, fast-paced videos, and non-detailed texts. We propose a novel Prototype-based Aleatoric Uncertainty Quantification (PAU) framework to provide trustworthy predictions by quantifying the uncertainty arisen from the inherent data ambiguity.
  arXiv  Detail & Related papers  (2023-09-29T09:41:19Z)
• Principled Knowledge Extrapolation with GANs [92.62635018136476]
  We study counterfactual synthesis from a new perspective of knowledge extrapolation. We show that an adversarial game with a closed-form discriminator can be used to address the knowledge extrapolation problem. Our method enjoys both elegant theoretical guarantees and superior performance in many scenarios.
  arXiv  Detail & Related papers  (2022-05-21T08:39:42Z)
• Criterion for a state to be distillable via stochastic incoherent operations [0.0]
  We show that any mixed state can be distilled into a pure coherent state via incoherent operations (sIOs) We also analyze the reason why sIO is stronger than strictly incoherent operations when we use them to distill a coherent state.
  arXiv  Detail & Related papers  (2021-12-12T06:37:42Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)

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.