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Activation of post-quantum steering

Ana Belén Sainz, Paul Skrzypczyk, Matty J. Hoban

TL;DR

The paper shows that post-quantum EPR steering, which may not be observable as post-quantum correlations in a simple Bell test, can be activated within a four-party network to yield post-quantum correlations. It achieves this by self-testing a bipartite assemblage between Charlie and Dani, encoding a parametric mixture with a transpose, and then transforming steering data into a Tsirelson-type Bell inequality that witnesses post-quantum correlations when Charlie and Dani perform joint measurements. The work extends to higher dimensions via qudit embeddings and synchronized self-testing, providing a universal activation mechanism and a resource-theoretic framing that connects steering with nonlocality in networks. These results offer new insight into how quantum and post-quantum resources interact and may inform foundational principles distinguishing quantum theory from broader physical theories.

Abstract

There are possible physical theories that give greater violations of Bell's inequalities than the corresponding Tsirelson bound, termed post-quantum non-locality. Such theories do not violate special relativity, but could give an advantage in certain information processing tasks. There is another way in which entangled quantum states exhibit non-classical phenomena, with one notable example being Einstein-Podolsky-Rosen (EPR) steering; a violation of a bipartite Bell inequality implies EPR steering, but the converse is not necessarily true. The study of post-quantum EPR steering is more intricate, but it has been shown that it does not always imply post-quantum non-locality in a conventional Bell test. In this work we show how to distribute resources in a larger network that individually do not demonstrate post-quantum non-locality but violate a Tsirelson bound for the network. That is, we show how to activate post-quantum steering so that it can now be witnessed as post-quantum correlations in a Bell scenario. One element of our work that may be of independent interest is we show how to self-test a bipartite quantum assemblage in a network, even assuming post-quantum resources.

Activation of post-quantum steering

TL;DR

The paper shows that post-quantum EPR steering, which may not be observable as post-quantum correlations in a simple Bell test, can be activated within a four-party network to yield post-quantum correlations. It achieves this by self-testing a bipartite assemblage between Charlie and Dani, encoding a parametric mixture with a transpose, and then transforming steering data into a Tsirelson-type Bell inequality that witnesses post-quantum correlations when Charlie and Dani perform joint measurements. The work extends to higher dimensions via qudit embeddings and synchronized self-testing, providing a universal activation mechanism and a resource-theoretic framing that connects steering with nonlocality in networks. These results offer new insight into how quantum and post-quantum resources interact and may inform foundational principles distinguishing quantum theory from broader physical theories.

Abstract

There are possible physical theories that give greater violations of Bell's inequalities than the corresponding Tsirelson bound, termed post-quantum non-locality. Such theories do not violate special relativity, but could give an advantage in certain information processing tasks. There is another way in which entangled quantum states exhibit non-classical phenomena, with one notable example being Einstein-Podolsky-Rosen (EPR) steering; a violation of a bipartite Bell inequality implies EPR steering, but the converse is not necessarily true. The study of post-quantum EPR steering is more intricate, but it has been shown that it does not always imply post-quantum non-locality in a conventional Bell test. In this work we show how to distribute resources in a larger network that individually do not demonstrate post-quantum non-locality but violate a Tsirelson bound for the network. That is, we show how to activate post-quantum steering so that it can now be witnessed as post-quantum correlations in a Bell scenario. One element of our work that may be of independent interest is we show how to self-test a bipartite quantum assemblage in a network, even assuming post-quantum resources.
Paper Structure (9 sections, 1 theorem, 26 equations, 3 figures)

This paper contains 9 sections, 1 theorem, 26 equations, 3 figures.

Table of Contents

  1. Einstein-Podolsky-Rosen scenarios
  2. Self-testing assemblages
  3. Tsirelson-Bell inequalities from steering inequalities
  4. Towards a proof of Eq. \ref{['pseudobell']}
  5. Summary and discussions
  6. Self-testing in post-quantum scenarios
  7. Tsirelson-Bell inequalities from steering inequalities -- getting rid of assumptions (ii) and (iv)
  8. Activation of post-quantum steering for higher-dimensional assemblages
  9. Derivation of the Independence Assumption for $r \in \{0,1\}$

Key Result

Theorem 1

Consider an assemblage with elements $\{\sigma_{abd|xyw}\}$ prepared in Charlie's Hilbert space $\mathcal{H}_{C}\otimes\mathcal{H}_{C'}$ after outputs produced by Alice, Bob, and Dani. If the following are satisfied by this assemblage: For such an assemblage, it then follows that

Figures (3)

  • Figure 1: Depiction of a tripartite EPR steering scenario, involving two sets of uncharacterised devices (Alice and Bob), and one set of characterised devices (Charlie). The measurements made by Alice and Bob 'steer' the state of Charlie, which is fully captured by the set of sub-normalised states $\sigma_{ab|xy}$ (referred to as an 'assemblage').
  • Figure 2: If we assume that Charlie performs measurements labelled by $z$, with outcomes labelled by $c$, then an assemblage $\sigma_{ab|xy}$ leads to correlations $p(abc|xyz)$.
  • Figure 3: The novel network scenario considered in this work. We consider a second assemblage shared between Charlie and Dani, and allow Charlie to perform joint measurements on both of his systems, producing correlations $p(abcd|xyzw)$. Our main result is to show that every post-quantum assemblage will lead to post-quantum correlations in this network configuration.

Theorems & Definitions (2)

  • Theorem 1
  • proof