Non-locality and steering are both non-classical phenomena witnessed in nature as a result of quantum entanglement. It is now well-established that one can study non-locality independently of the formalism of quantum mechanics, in the so-called device-independent framework. With regards to steering, although one cannot study it completely independently of the quantum formalism, ‘post-quantum steering’ has been described, which is steering that cannot be reproduced by measurements on entangled states but does not lead to superluminal signalling. In this work we present a framework based on the study of quantum channels in which one can study steering (and non-locality) in quantum theory and beyond. In this framework, we show that kinds of steering, whether quantum or post-quantum, are directly related to particular families of quantum channels that have been previously introduced by Beckman et al (2001 Phys. Rev. A 64 052309). Utilizing this connection we also demonstrate new analytical examples of post-quantum steering, give a quantum channel interpretation of almost quantum non-locality and steering, easily recover and generalize the celebrated Gisin–Hughston–Jozsa–Wootters theorem, and initiate the study of post-quantum Buscemi non-locality and non-classical teleportation. In this way, we see post-quantum non-locality and steering as just two aspects of a more general phenomenon.
Non-locality and steering are both non-classical phenomena witnessed in nature as a result of quantum entanglement. It is now well-established that one can study non-locality independently of the formalism of quantum mechanics, in the so-called device-independent framework. With regards to steering, although one cannot study it completely independently of the quantum formalism, ‘post-quantum steering’ has been described, which is steering that cannot be reproduced by measurements on entangled states but does not lead to superluminal signalling. In this work we present a framework based on the study of quantum channels in which one can study steering (and non-locality) in quantum theory and beyond. In this framework, we show that kinds of steering, whether quantum or post-quantum, are directly related to particular families of quantum channels that have been previously introduced by Beckman et al (2001 Phys. Rev. A 64 052309). Utilizing this connection we also demonstrate new analytical examples of post-quantum steering, give a quantum channel interpretation of almost quantum non-locality and steering, easily recover and generalize the celebrated Gisin–Hughston–Jozsa–Wootters theorem, and initiate the study of post-quantum Buscemi non-locality and non-classical teleportation. In this way, we see post-quantum non-locality and steering as just two aspects of a more general phenomenon.
Non-locality and steering are both non-classical phenomena witnessed in nature as a result of quantum entanglement. It is now well-established that one can study non-locality independently of the formalism of quantum mechanics, in the so-called device-independent framework. With regards to steering, although one cannot study it completely independently of the quantum formalism, 'post-quantum steering' has been described, which is steering that cannot be reproduced by measurements on entangled states but does not lead to superluminal signalling. In this work we present a framework based on the study of quantum channels in which one can study steering (and non-locality) in quantum theory and beyond. In this framework, we show that kinds of steering, whether quantum or post-quantum, are directly related to particular families of quantum channels that have been previously introduced by Beckman et al (2001 Phys. Rev. A 64 052309). Utilizing this connection we also demonstrate new analytical examples of post-quantum steering, give a quantum channel interpretation of almost quantum non-locality and steering, easily recover and generalize the celebrated Gisin–Hughston–Jozsa–Wootters theorem, and initiate the study of post-quantum Buscemi non-locality and non-classical teleportation. In this way, we see post-quantum non-locality and steering as just two aspects of a more general phenomenon.
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.
We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models, which will be defined in this work. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone.
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 steering means that in some bipartite quantum systems, the local measurements on one side can determine the state of the other side. Here we show that in high-dimensional systems, there exists a specific entangled state which can display a kind of chaos effect when being adopted for steering. That is, a subtle difference in the measurement results on one side can steer the other side into completely orthogonal states. Moreover, by expanding the result to infinite-dimensional systems, we find two sets of states for which, contrary to common belief, even though their density matrices approach being identical, the steering between them is impossible. This property makes them very useful for quantum cryptography.
Quantum steering is a kind of quantum feature between quantum entanglement and Bell non-locality. Due to its special asymmetry, quantum steering plays an important role in many aspects of quantum information processing and thus has been widely concerned. There are many contributions on quantum steering in bipartite systems up to now, while tripartite systems have more complex structures than bipartite systems and then have more diversified steering scenarios. In this paper, two types of quantum steering scenarios are introduced for a tripartite quantum system, named “one-sided device-independent steering" and “two-sided device-independent steering". Each of them contains two levels according to the separability of the local hidden states and the independence of the local hidden variables, respectively. Based on giving the mathematical definitions of these steering scenarios, some necessary and sufficient conditions for a state to be unsteerable are obtained and sufficient conditions for a state to be steerable are also established.