Maximal Secret Reconstruction, Teleportation and Bell's Inequality

• URL: http://arxiv.org/abs/2404.01212v2
• Date: Thu, 18 Apr 2024 11:20:30 GMT
• Title: Maximal Secret Reconstruction, Teleportation and Bell's Inequality
• Abstract summary: We characterize a secret shareable state in a pure three-qubit system. We find that all secret shareable states satisfy Bell's inequality in both dealer--reconstructor and dealer--assistant partitions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A tripartite state is said to be a potential resource for secret sharing if the state imposes restrictions on the teleportation fidelity of the bipartite dealer--reconstructor and dealer--assistant channels in addition of being useful for the state reconstruction. Given a secret shareable state in a pure three-qubit system, we are able to characterize the set of states with maximum possible reconstruction fidelity (abbreviated as MSR states) for a fixed value of the maximum teleportation fidelity that can be obtained out of both the dealer--receiver channels. Similarly for a value giving the maximum of Bell-CHSH value of both dealer--reconstructor and dealer--assistant channels, we are able to find the maximum achievable reconstruction fidelity. Interestingly, we find that all secret shareable states satisfy Bell's inequality in both dealer--reconstructor and dealer--assistant partitions. This brings out a new mutual exclusivity between secret shareable state and Bell's inequality violations. Our result paves the way in identifying the best candidate among the secret sharing resource states in achieving the maximum reconstruction fidelity thus by setting the practical information transfer limit in a possible resource theoretic extension of secret sharing. It also brings out a new kind of mutual exclusiveness between the bipartite correlation and in the ability of secret sharing in a tripartite setting.

Related papers

• Symmetric $N \ o M$ telecloning and remote quantum state inference [2.8201809312429744]
  We show that symmetric $N to M$ telecloning can be probabilistically performed using only sequential (or parallel) Bell state measurements.<n>When successful, the fidelity of each receiver's reduced state saturates the bound imposed by the no-cloning theorem.<n>Surprisingly, we uncover that, at a given of the protocol, pairwise entanglement is not always necessary to increase the teleportation fidelity.
  arXiv  Detail & Related papers  (2026-08-18T18:07:52Z)
• How to reconstruct (anonymously) a secret cellular automaton [1.018462284491991]
  We consider threshold secret sharing schemes based on cellular automata (CA) that allows for anonymous reconstruction.<n>We show that the new resulting scheme enables anonymous reconstruction of secret CA rules.
  arXiv  Detail & Related papers  (2026-04-13T12:04:06Z)
• Revocation and Reconstruction of Shared Quantum States [0.0]
  We show an independent way to revoke, if, for any reason, the dealer is not sure about the intention of the reconstructor.<n>We further consider a class of four qubit pure entangled states as resource and explicitly find the range of parameters for which the protocol will be successful.
  arXiv  Detail & Related papers  (2025-11-07T13:00:27Z)
• Limiting one-way distillable secret key via privacy testing of extendible states [11.199585259018457]
  In this paper, we determine the maximum probability with which an arbitrary $k$-extendible state can pass a privacy test.<n>We also prove that it is equal to the maximum fidelity between an arbitrary $k$-extendible state and the standard maximally entangled state.<n>For some key examples of interest, our bounds are significantly tighter than other known efficiently computable bounds.
  arXiv  Detail & Related papers  (2025-11-06T15:11:54Z)
• Optimality of universal conclusive entanglement purification protocols [75.52645767671567]
  We establish fundamental limits for conclusive protocols distilling perfect Bell states from a pure two-qubit states.<n>We prove that a known protocol achieves these bounds, confirming its optimality.
  arXiv  Detail & Related papers  (2025-09-11T13:04:17Z)
• Information Bargaining: Bilateral Commitment in Bayesian Persuasion [60.3761154043329]
  We introduce a unified framework and a well-structured solution concept for long-term persuasion.<n>This perspective makes explicit the common knowledge of the game structure and grants the receiver comparable commitment capabilities.<n>The framework is validated through a two-stage validation-and-inference paradigm.
  arXiv  Detail & Related papers  (2025-06-06T08:42:34Z)
• Quantum cloning transformation unlocks the potential of W class of states in a secret sharing protocol [0.0]
  We introduce a quantum secret sharing protocol exploiting a three-qubit W class of state shared between three parties. We find that the protocol is probabilistic and have calculated the probability of success of the protocol. Even a less entangled W class of state can also play a vital role in the proposed secret-sharing scheme.
  arXiv  Detail & Related papers  (2024-08-13T08:27:58Z)
• Non-Adaptive Coding for Two-Way Wiretap Channel with or without Cost Constraints [45.65636963872864]
  We study the secrecy results for the two-way wiretap channel (TW-WC) with an external eavesdropper under a strong secrecy metric. We derive inner bounds on the secrecy capacity regions for the TW-WC under strong joint and individual secrecy constraints.
  arXiv  Detail & Related papers  (2023-10-21T01:05:59Z)
• Quantum Secret Reconstruction [2.8233507229238177]
  This paper proposes the first quantum secret reconstruction protocol based on cluster states. It is shown that the proposed protocol is secure against several common attacks.
  arXiv  Detail & Related papers  (2023-06-15T05:24:29Z)
• Accelerating Reinforcement Learning with Value-Conditional State Entropy Exploration [97.19464604735802]
  A promising technique for exploration is to maximize the entropy of visited state distribution. It tends to struggle in a supervised setup with a task reward, where an agent prefers to visit high-value states. We present a novel exploration technique that maximizes the value-conditional state entropy.
  arXiv  Detail & Related papers  (2023-05-31T01:09:28Z)
• Multipartite entanglement theory with entanglement-nonincreasing operations [91.3755431537592]
  We extend the resource theory of entanglement for multipartite systems beyond the standard framework of local operations and classical communication. We demonstrate that in this adjusted framework, the transformation rates between multipartite states are fundamentally dictated by the bipartite entanglement entropies of the respective quantum states.
  arXiv  Detail & Related papers  (2023-05-30T12:53:56Z)
• Controlled State Reconstruction and Quantum Secret Sharing [0.0]
  We present a benchmark for resource characterization in the process of controlled quantum state reconstruction and secret sharing. We formulate the idea of quantum advantage in approximate state reconstruction as surpassing the classical limit set at 2/3. This article brings out new interoperability between teleportation and state reconstruction.
  arXiv  Detail & Related papers  (2023-05-10T11:30:30Z)
• Revocation and Reconstruction of Shared Quantum Secrets [0.5735035463793007]
  In existing protocols there are no means by which the dealer can retrieve back the secret once he/she finds all the share holders to be semi-honest. In this work, we explicitly deal with shareholders who are semi-honest and not dishonest. Our protocol makes a significant advancement in solving this problem by designing strategy in bringing back the secret in the worst possible situation.
  arXiv  Detail & Related papers  (2021-12-31T17:08:12Z)
• Heterogeneous Multipartite Entanglement Purification for Size-Constrained Quantum Devices [68.8204255655161]
  Purifying entanglement resources after their imperfect generation is an indispensable step towards using them in quantum architectures. Here we depart from the typical purification paradigm for multipartite states explored in the last twenty years. We find that smaller sacrificial' states, like Bell pairs, can be more useful in the purification of multipartite states than additional copies of these same states.
  arXiv  Detail & Related papers  (2020-11-23T19:00:00Z)
• Entanglement purification by counting and locating errors with entangling measurements [62.997667081978825]
  We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about number and positions of errors in the noisy ensemble.
  arXiv  Detail & Related papers  (2020-11-13T19:02:33Z)
• Study on Entanglement and its Utility in Information Processing [0.0]
  The efficacies of maximally and that of non-maximally entangled mixed states as teleportation channels have been studied. A new class of non-maximally entangled mixed states have been proposed also. Their advantages as quantum teleportation channels over existing non-maximally entangled mixed states have been verified.
  arXiv  Detail & Related papers  (2020-07-21T15:28:26Z)
• Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction [64.04327674866464]
  We introduce a variant of randomness extraction framework where free incoherent operations are allowed before the incoherent measurement. We show that the maximum number of random bits extractable from a given quantum state is precisely equal to the maximum number of coherent bits that can be distilled from the same state. Remarkably, the incoherent operation classes all admit the same second order expansions.
  arXiv  Detail & Related papers  (2020-02-27T09:48:52Z)
• Quantum secret sharing using GHZ state qubit positioning and selective qubits strategy for secret reconstruction [4.378411442784295]
  The work presents a novel quantum secret sharing strategy based on GHZ product state sharing between three parties. Unlike the other protocols, this protocol does not involve the entire initial state reconstruction, rather uses selective qubits to discard the redundant qubits at the time of reconstruction to decrypt the secret. The protocol also allows for security against malicious attacks by an adversary without affecting the integrity of the secret.
  arXiv  Detail & Related papers  (2020-02-21T08:45:07Z)
• Permutation Enhances Classical Communication Assisted by Entangled States [67.12391801199688]
  We show that the capacity satisfies the strong converse property and thus the formula serves as a sharp dividing line between achievable and unachievable rates of communication. As examples, we derive analytically the classical capacity of various quantum channels of interests.
  arXiv  Detail & Related papers  (2020-01-07T01:49:31Z)

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.