Semi-device-independent certification of indefinite causal order

@article{Bavaresco2019SemideviceindependentCO,
  title={Semi-device-independent certification of indefinite causal order},
  author={Jessica Bavaresco and Mateus Ara'ujo and {\vC}aslav Brukner and Marco T'ulio Quintino},
  journal={Quantum},
  year={2019}
}
When transforming pairs of independent quantum operations according to the fundamental rules of quantum theory, an intriguing phenomenon emerges: some such higher-order operations may act on the input operations in an indefinite causal order. Recently, the formalism of process matrices has been developed to investigate these noncausal properties of higher-order operations. This formalism predicts, in principle, statistics that ensure indefinite causal order even in a device-independent scenario… 

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References

SHOWING 1-10 OF 105 REFERENCES
Experimental verification of an indefinite causal order
TLDR
Researchers report the first decisive demonstration of a process with an indefinite causal order, and experimentally determine a causal witness, demonstrating by almost 7 SDs that the experimentally implemented process does not have a definite causal order.
Quantum circuits with classical versus quantum control of causal order
Quantum supermaps are transformations that map quantum operations to quantum operations. It is known that quantum supermaps which respect a definite, predefined causal order between their input
A purification postulate for quantum mechanics with indefinite causal order
TLDR
A purification postulate is proposed: processes are physical only if they are purifiable, and necessary conditions for a process to be purifiable are derived, and several known processes do not satisfy them.
Witnesses of causal nonseparability: an introduction and a few case studies
TLDR
This work presents a shorter introduction to the concept of witnesses of causal nonseparability, and focuses on some explicit examples—by considering in particular different noise models for the quantum switch—to show how to construct and use such witnesses in practice.
Experimental Entanglement of Temporal Orders
The study of causal relations, a cornerstone of physics, has recently been applied to the quantum realm, leading to the discovery that not all quantum processes have a definite causal structure.
Quantum correlations with no causal order
TLDR
It is shown that in a classical limit causal order always arises, which suggests that space-time may emerge from a more fundamental structure in a quantum-to-classical transition.
Experimentally feasible computational advantage from quantum superposition of gate orders
TLDR
Tasks (1) for which there is a provable computational advantage of a quantum-controlled ordering of gates in the asymptotic case and (2) that require only qubit gates are introduced, suitable to demonstrate this advantage experimentally.
Witnessing causal nonseparability
TLDR
This work shows that a recently demonstrated resource for quantum computation—the quantum switch—is a genuine example of 'indefinite causal order', and introduces a new tool—the causal witness—which can detect the causal nonseparability of any quantum resource that is incompatible with a definite causal order.
Indefinite Causal Order in a Quantum Switch.
TLDR
A photonic quantum switch is realized, where two operations A and B act in a quantum superposition of their two possible orders, on the transverse spatial mode of the photons; polarization coherently controls their order.
Quantum Metrology with Indefinite Causal Order.
TLDR
This work addresses the study of quantum metrology enhanced by indefinite causal order, demonstrating a quadratic advantage in the estimation of the product of two average displacements in a continuous variable system and proves that no setup can have root-mean-square error vanishing faster than the Heisenberg limit 1/N.
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