Minh Cong Tran

Quantum entanglement from random measurements

We show that the expectation value of squared correlations measured along random local directions is an identifier of quantum entanglement in pure states which can be directly experimentally assessed if two copies of the state were available. Entanglement can therefore be detected by parties who do not share a common reference frame and whose local reference frames, such as polarisers or Stern-Gerlach magnets, remain unknown. Furthermore, we also show that in every experimental run access to only one qubit from the macroscopic reference is sufficient to identify entanglement, violate a Bell inequality, and in fact observe all phenomena observable with macroscopic references. Finally, we provide a state-independent entanglement witness solely in terms of random correlations and emphasise how data gathered for a single random measurement setting per party reliably detects entanglement. This is only possible due to utilised randomness and should find practical applications in experimental confirmation of multi-photon entanglement or space experiments.

Correlations between outcomes of random measurements

We recently showed that multipartite correlations between outcomes of random observables detect quantum entanglement in all pure and some mixed states. In this followup article we further develop this approach, derive a maximal amount of such correlations, and show that they are not monotonous under local operations and classical communication. Nevertheless, we demonstrate their usefulness in entanglement detection with a single random observable per party. Finally we study convex-roof extension of the correlations and provide a closed-form necessary and sufficient condition for entanglement in rank-2 mixed states and a witness in general.

Genuine Multipartite Entanglement without Multipartite Correlations

Nonclassical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are n-particle states which do not exhibit n-partite correlations at all but still are genuinely n-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without multipartite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local realistic model describing their properties.

The Werner gap in the presence of simple coloured noise

The ‘Werner gap’ is the range of relevant parameters characterizing a quantum state for which it is both entangled and admits a local hidden variable model. Werner showed that the gap becomes maximal for entanglement mixed with white noise if subsystems have infinitely many levels. Here we study pure entangled states mixed with simple coloured noise modelled as a single pure product state. We provide an explicit local hidden variable model for quantum correlations of some states of this family and provide hints that there is probably a model for all quantum predictions. This demonstrates essentially a maximal Werner gap already for just two qubits. Additionally to its fundamental interest, the study has implications for quantum computation and communication.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.

Lieb-Robinson bounds on n -partite connected correlation functions

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.