Local-Data-Hiding and Causal Inseparability: Probing Indefinite Causal Structures with Cryptographic Primitives

• URL: http://arxiv.org/abs/2407.20543v1
• Date: Tue, 30 Jul 2024 04:54:03 GMT
• Title: Local-Data-Hiding and Causal Inseparability: Probing Indefinite Causal Structures with Cryptographic Primitives
• Authors: Sahil Gopalkrishna Naik, Samrat Sen, Ram Krishna Patra, Ananya Chakraborty, Mir Alimuddin, Manik Banik, Pratik Ghosal,
• Abstract summary: Recent studies suggest the possibility of indefiniteness in causal structure, which emerges as a novel information primitive. We show that agents embedded in an indefinite causal structure can outperform their counterparts operating in a definite causal background. We report an intriguing super-activation phenomenon, where two quantum processes, each individually not useful for the LBH task, become useful when used together.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Formulation of physical theories typically assumes a definite causal structure -- either static or dynamic -- among the set of physical events. Recent studies, however, suggest the possibility of indefiniteness in causal structure, which emerges as a novel information primitive offering advantages in various protocols. In this work, we explore utilities of this new primitive in cryptographic applications. To this aim, we propose a task called local-data-hiding, where a referee distributes encrypted messages among distant parties in such a way that the parties individually remain completely ignorant about the messages, and thus try to decrypt their respective messages through mutual collaboration. As we demonstrate, agents embedded in an indefinite causal structure can outperform their counterparts operating in a definite causal background. Considering the bipartite local-bit-hiding (LBH) task, we establish a strict duality between its optimal success probability and the optimal violation of a causal inequality obtained from the guess-your-neighbour's-input game. This, in turn, provides a way forward to obtain Tsirelson-type bounds for causal inequalities. Furthermore, similar to Peres's separability criterion, we derive a necessary criterion for quantum processes to be useful in the LBH task. We then report an intriguing super-activation phenomenon, where two quantum processes, each individually not useful for the LBH task, become useful when used together. We also analyze the utility of causal indefiniteness arising in classical setups and show its advantages in multipartite variants of the local-data-hiding task. Along with establishing new cryptographic applications our study illuminates various unexplored aspects of causal indefiniteness, and welcomes further studies on this new information primitive.

Related papers

• Rethinking State Disentanglement in Causal Reinforcement Learning [78.12976579620165]
  Causality provides rigorous theoretical support for ensuring that the underlying states can be uniquely recovered through identifiability. We revisit this research line and find that incorporating RL-specific context can reduce unnecessary assumptions in previous identifiability analyses for latent states. We propose a novel approach for general partially observable Markov Decision Processes (POMDPs) by replacing the complicated structural constraints in previous methods with two simple constraints for transition and reward preservation.
  arXiv  Detail & Related papers  (2024-08-24T06:49:13Z)
• New Rules for Causal Identification with Background Knowledge [59.733125324672656]
  We propose two novel rules for incorporating BK, which offer a new perspective to the open problem. We show that these rules are applicable in some typical causality tasks, such as determining the set of possible causal effects with observational data.
  arXiv  Detail & Related papers  (2024-07-21T20:21:21Z)
• Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks [0.0]
  We use analytical and numerical tools to estimate robustness of contextuality in POM scenarios under different types of noise. We obtain a general relation between robustness of contextuality to depolarisation and the success rate in any $n$-to-1 POM scenario.
  arXiv  Detail & Related papers  (2024-06-18T16:43:43Z)
• Identifiable Latent Neural Causal Models [82.14087963690561]
  Causal representation learning seeks to uncover latent, high-level causal representations from low-level observed data. We determine the types of distribution shifts that do contribute to the identifiability of causal representations. We translate our findings into a practical algorithm, allowing for the acquisition of reliable latent causal representations.
  arXiv  Detail & Related papers  (2024-03-23T04:13:55Z)
• Alternative robust ways of witnessing nonclassicality in the simplest scenario [0.0]
  We relate notions of nonclassicality in the simplest nontrivial scenario. We use an approach based on the notion of bounded ontological distinctness for preparations. As an application of our findings, we treat the case of two-bit parity-oblivious multiplexing in the presence of noise.
  arXiv  Detail & Related papers  (2023-11-22T15:41:34Z)
• Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario [0.0]
  We present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to provide lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy. Our results demonstrate the first experiment that certifies close to two bits of randomness from binary measurements of two parties.
  arXiv  Detail & Related papers  (2023-03-13T20:42:53Z)
• Fairness and robustness in anti-causal prediction [73.693135253335]
  Robustness to distribution shift and fairness have independently emerged as two important desiderata required of machine learning models. While these two desiderata seem related, the connection between them is often unclear in practice. By taking this perspective, we draw explicit connections between a common fairness criterion - separation - and a common notion of robustness.
  arXiv  Detail & Related papers  (2022-09-20T02:41:17Z)
• Discovering Latent Causal Variables via Mechanism Sparsity: A New Principle for Nonlinear ICA [81.4991350761909]
  Independent component analysis (ICA) refers to an ensemble of methods which formalize this goal and provide estimation procedure for practical application. We show that the latent variables can be recovered up to a permutation if one regularizes the latent mechanisms to be sparse.
  arXiv  Detail & Related papers  (2021-07-21T14:22:14Z)
• Nested Counterfactual Identification from Arbitrary Surrogate Experiments [95.48089725859298]
  We study the identification of nested counterfactuals from an arbitrary combination of observations and experiments. Specifically, we prove the counterfactual unnesting theorem (CUT), which allows one to map arbitrary nested counterfactuals to unnested ones.
  arXiv  Detail & Related papers  (2021-07-07T12:51:04Z)

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.