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Topologically noise robust network steering without inputs

Dhruv Baheti, Shubhayan Sarkar

TL;DR

The paper addresses observing quantum steering and nonlocality in networks without full inputs or strict independence assumptions by introducing swap-steering in triangle and general n-ring networks with a single trusted node. It develops linear witnesses to detect swap-steering, proves a separable-hidden-state bound of ${eta_{SOHS}=1/2}$, and shows a concrete quantum scheme achieving the algebraic maximum ${W=1}$ in the triangle, plus a scalable maximal violation for any n with the same strategy. A weak self-testing result certifies the states and measurements under plausible assumptions, and the framework is extended to topologically robust scenarios where untrusted parts may be arbitrarily connected, yet still exhibit a quantum advantage. Importantly, when the trusted party has tomography, every bipartite entangled state can generate swap-steerable correlations in the n-ring network, broadening the scope of detectable quantum correlations in networks. Collectively, these results provide a topologically robust, noise-tolerant route to network quantum advantage with reduced reliance on network structure and iid assumptions, with potential implications for secure quantum networking tasks.

Abstract

Quantum networks with independent sources allow observing quantum nonlocality or steering with just a single measurement per node of the network, or without any inputs. Inspired by the recently introduced notion of swap-steering, we consider here the triangle network scenario without inputs, where one of the parties is trusted to perform a well-calibrated measurement. In this scenario, we first propose a linear witness to detect triangle network swap-steering. Then, by using the correlations that achieve the maximum value of this inequality, and assuming that all the sources are the same, we can self-test the state generated by the sources and the measurements of the untrusted party. We then extend this framework to ring networks with an arbitrary number of nodes with one of them being trusted. Interestingly, this is the first example of a topologically robust, that is, one can observe steerability without assuming the network structure of the network, as well as noise-robust quantum advantage in a network. Additionally, by allowing the trusted party to perform tomography of their subsystems, we demonstrate that every bipartite entangled state will result in swap-steerable correlations in the ring network. For this purpose, we construct linear witnesses to detect ring network swap-steering corresponding to every bipartite entangled state.

Topologically noise robust network steering without inputs

TL;DR

The paper addresses observing quantum steering and nonlocality in networks without full inputs or strict independence assumptions by introducing swap-steering in triangle and general n-ring networks with a single trusted node. It develops linear witnesses to detect swap-steering, proves a separable-hidden-state bound of , and shows a concrete quantum scheme achieving the algebraic maximum in the triangle, plus a scalable maximal violation for any n with the same strategy. A weak self-testing result certifies the states and measurements under plausible assumptions, and the framework is extended to topologically robust scenarios where untrusted parts may be arbitrarily connected, yet still exhibit a quantum advantage. Importantly, when the trusted party has tomography, every bipartite entangled state can generate swap-steerable correlations in the n-ring network, broadening the scope of detectable quantum correlations in networks. Collectively, these results provide a topologically robust, noise-tolerant route to network quantum advantage with reduced reliance on network structure and iid assumptions, with potential implications for secure quantum networking tasks.

Abstract

Quantum networks with independent sources allow observing quantum nonlocality or steering with just a single measurement per node of the network, or without any inputs. Inspired by the recently introduced notion of swap-steering, we consider here the triangle network scenario without inputs, where one of the parties is trusted to perform a well-calibrated measurement. In this scenario, we first propose a linear witness to detect triangle network swap-steering. Then, by using the correlations that achieve the maximum value of this inequality, and assuming that all the sources are the same, we can self-test the state generated by the sources and the measurements of the untrusted party. We then extend this framework to ring networks with an arbitrary number of nodes with one of them being trusted. Interestingly, this is the first example of a topologically robust, that is, one can observe steerability without assuming the network structure of the network, as well as noise-robust quantum advantage in a network. Additionally, by allowing the trusted party to perform tomography of their subsystems, we demonstrate that every bipartite entangled state will result in swap-steerable correlations in the ring network. For this purpose, we construct linear witnesses to detect ring network swap-steering corresponding to every bipartite entangled state.

Paper Structure

This paper contains 17 sections, 2 theorems, 75 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Triangle network swap-steering
  3. Swap-Steering
  4. Necessary conditions for swap-steering
  5. Weak self-testing in the triangle network
  6. $n$-ring scenario
  7. Topologically Robust Swap Steering
  8. All bipartite entangled states generate swap-steering correlations in the $n-$ring network
  9. Discussions
  10. Acknowledgements
  11. Proofs in the Triangle scenario
  12. Noise tolerance analysis
  13. Triangle network weak self-testing
  14. Proofs for the $n-$ring scenario
  15. SOHS and quantum bounds of $n-$party swap steering witness
  16. ...and 2 more sections

Key Result

Theorem 1

Assume that Alice, Bob and Charlie observe that the correlations $p(a,b,c)$ in the steering functional $W_3$steering-3 are equal along with $W_3=1$ such that trusted Alice performs the Bell-basis. Considering identical sources, such that the states generated by them are pure and measurements of untr 2. The measurement of Bob $\{M_{A_2}^{a_2}\}$ and Charlie $\{M_{A_3}^{a_3}\}$ is certified as f

Figures (2)

  • Figure 1: Triangle swap-steering scenario. Each node receives two subsystems from the two sources connected to them, on which a single four-outcome measurement is performed. Node $A_1$ is trusted here, meaning a Bell-basis measurement is performed at this node. No communication is allowed between the nodes during the experiment. By repeatedly performing the experiment, one obtains the joint probability distribution $\{p(a_1,a_2,a_3)\}$.
  • Figure 2: (left) Hexagonal swap-steering scenario. (right) $n-$ring topologically robust swap-steering scenario. In both scenarios, the node $A_1$ is trusted to perform measurement in the Bell-basis and all other parties perform a single four outcome measurement. In the left scenario, $A_i$ receive subsystems from sources $\lambda_{i-1},\lambda_i$. However, in the right one all the parties $A_2, \ldots,A_n$ can do any operation among themselves to produce the outputs $(a_2,\ldots,a_n)$. After the experiment, they construct the joint distribution $p(\{a\})$.

Theorems & Definitions (7)

  • Theorem 1
  • Theorem 1
  • proof
  • proof
  • proof
  • proof
  • proof