The study of stronger-than-quantum effects is a fruitful line of research that provides valuable insight into quantum theory. Unfortunately, traditional bipartite steering scenarios can always be explained by quantum theory. Here, we show that, by relaxing this traditional setup, bipartite steering incompatible with quantum theory is possible. The two scenarios we describe, which still feature Alice remotely steering Bob's system, are (i) one where Bob also has an input and operates on his subsystem, and (ii) the "instrumental steering" scenario. We show that such bipartite postquantum steering is a genuinely new type of postquantum nonlocality, which does not follow from postquantum Bell nonlocality. In addition, we present a method to bound quantum violations of steering inequalities in these scenarios.
The study of stronger-than-quantum effects is a fruitful line of research that provides valuable insight into quantum theory. Unfortunately, traditional bipartite steering scenarios can always be explained by quantum theory. Here, we show that, by relaxing this traditional setup, bipartite steering incompatible with quantum theory is possible. The two scenarios we describe, which still feature Alice remotely steering Bob's system, are (i) one where Bob also has an input and operates on his subsystem, and (ii) the "instrumental steering" scenario. We show that such bipartite postquantum steering is a genuinely new type of postquantum nonlocality, which does not follow from postquantum Bell nonlocality. In addition, we present a method to bound quantum violations of steering inequalities in these scenarios.
The study of stronger-than-quantum phenomena (i.e., postquantum) has enabled a deeper understanding of the scope of quantum theory. Much is known about the case of correlations in Bell scenarios, where the device-independent framework allowed us to explore its possibilities independently of the formalism of quantum theory. However, less is known about the phenomenon of Einstein-Podolsky-Rosen steering. Here, the `characterised parties' are assumed to describe their systems locally through the quantum formalism, which inconveniences a theory-independent description. In addition, a theorem by Gisin and Hughston, Josza and Wootters further hindered the discovery of the phenomenon. The study of postquantum steering, initiated about a decade ago, has been quite fruitful, including: the development of mathematical formalisms that frame the effect, resource theories that quantify it as a resource, and activation protocols that relate it to Bell correlations. However, all these results have a limitation in common: they apply to scenarios with only one quantum party.
Here we articulate the concept of postquantum steering for scenarios with multiple quantum parties, bringing in the missing piece to the puzzle. We provide an algorithm to certify postquantumness, which in some cases also certifies quantumness. We also define a hierarchy of semidefinite programs that bounds the set of quantum assemblages from the outside. Moreover, we show that the study of postquantum steering is fundamentally relevant since it is not just a mere mathematical curiosity allowed by the no-signalling principle, but it may arise within compositional theories beyond quantum theory. Our work further discovers a peculiarity of steering: its theory-independent description fundamentally prevents a direct connection with Bell nonlocality -- e.g., nonclassical Bell correlations do not imply nonclassical steering.
In a standard bipartite Einstein-Podolsky-Rosen (EPR) scenario, Alice and Bob share a system prepared in an entangled state and Alice performs local measurements. One possible generalization of this setup is to allow Bob to also locally process his subsystem. Then correlations generated in such generalized EPR scenarios are examples of nonsignaling bipartite resources, called assemblages, that can exhibit postquantum behavior, i.e., cannot be generated using solely quantum systems. There exist assemblages that, despite being postquantum resources, can only generate quantum correlations in bipartite Bell-type scenarios. Here we present a protocol for activation of postquantumness in bipartite generalized EPR scenarios such as the so-called Bob-with-input, measurement-device-independent, and channel EPR scenarios. By designing a protocol that involves distributing the assemblages in a larger network, we derive tailored Bell inequalities which can be violated beyond their quantum bound in this new setup. Our results show that in all of the above generalized scenarios, the postquantumness of the assemblages can be witnessed at the level of correlations they produce.
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.
Quantum nonlocality is a significant feature in quantum information theory, prompting recent investigations into the potential reuse of post-measurement states to uncover nonlocality among sequentially measuring observers. While prior studies primarily focused on bipartite or tripartite systems and observers with one chain, such as multiple Bobs with a single Alice or multiple Charlies with a single Alice and Bob, our work extends beyond this framework. We explore sequential nonlocality in systems comprising more parties and observer chains. Our findings reveal that in n-partite systems, regardless of whether it is a single-chain or double-chain scenario, there exist unbounded sequential observers capable of detecting nonlocality through violations of the Mermin inequality. In contrast to the conjecture that sequential Bell nonlocality cannot manifest with multiple Alices and Bobs in bipartite systems (i.e., the double-chain setting)[Phys. Rev. A 104, L060201 (2021)], our results suggest that increasing the number of subsystems may enable more observer chains to detect nonlocality alongside single observers. Our study advances research on sequential nonlocality, providing valuable insights into its detection across diverse scenarios.
This paper illustrates a direct connection between quantum steering and non-trivial preparation contextuality. In two party-two measurement per party-two outcomes per measurement (2−2−2) Bell scenario, any argument of Bell nonlocality is a proof of trivial preparation contextuality; however, the converse may not hold. If one of the parties (say, Alice) performs the measurements of more than two dichotomic observables, then it is possible to find a set of non-trivial functional relations between Alice's observables. We argue that the existence of a suitable set of such non-trivial relations between Alice's observables may warrant the unsteerability of quantum states at the end of another spatially separated party (say, Bob). Interestingly, such constraints can be read as non-trivial preparation non-contextuality assumptions in an ontological model. We further demonstrate two types of Bell inequalities that can be converted into linear steering inequalities using the aforementioned non-trivial conditions on Alice's observables. Such steering inequalities can also be considered as non-trivial preparation noncontextual inequalities. Since the local bound of the family of Bell expression gets reduced under the additional non-trivial conditions, it provides a test of quantum steering and nonlocality from the same family of Bell expressions depending upon its violation of the non-trivial preparation non-contextual or the local bound, thereby establishing a direct connection between quantum steering and non-trivial preparation contextuality.
We consider a quantum steering scenario where Alice prepares a bipartite state, sends one subsystem to Bob through a quantum channel, and aims to convince him that their shared state is entangled. Bob, however, will never be convinced if the channel is steering-breaking, that is, if the channel destroys steerability for any input state. To verify that a channel renders a state useless for demonstrating steering, one must consider all possible measurements performed by Alice and check if the conditional states Bob receives admit a local-hidden-state (LHS) model. This is generally a hard problem since it requires considering an infinite number of measurement combinations. Here, we show that the method proposed in [Phys. Rev. Lett. 117, 190401 (2016); Phys. Rev. Lett. 117, 190402 (2016)] can be utilized to tackle this problem. Furthermore, owing to the intimate relation between steering and measurement incompatibility, our approach can faithfully certify whether a channel destroys incompatibility for any set of measurements. Finally, we propose an experimental criterion for certifying steering- and incompatibility-breaking channels, which may be of independent interest.