Quantum Entanglement in High Dimensions

Manuel Erhard, Mario Krenn, Anton Zeilinger

Benjamin D. M. Jones, Roope Uola, Thomas Cope +4 more

The effect of quantum steering arises from the judicious combination of an entangled state with a set of incompatible measurements. Recently, it was shown that this form of quantum correlations can be quantified in terms of a dimension, leading to the notion of genuine high-dimensional steering. While this naturally connects to the dimensionality of entanglement (Schmidt number), we show that this effect also directly connects to a notion of dimension for measurement incompatibility. More generally, we present a general connection between the concepts of steering and measurement incompatibility, when quantified in terms of dimension. From this connection, we propose an alternative twist on the problem of simulating quantum correlations. Specifically, we show how the correlations of certain high-dimensional entangled states can be exactly recovered using only shared randomness and lower-dimensional entanglement. Finally, we derive criteria for testing the dimension of measurement incompatibility and discuss the extension of these ideas to quantum channels.

Karim Douhou, Salah Eddine Ennadifi, L. Jebli

Gabriele Cobucci, Armin Tavakoli

Complex forms of quantum entanglement can arise in two qualitatively different ways: either between many qubits or between two particles with higher-than-qubit dimension. While both the many-qubit frontier and the high-dimension frontier are well established, state-of-the-art quantum technology is becoming increasingly able to create and manipulate entangled states that simultaneously feature many particles and high dimension. Here, we investigate generic states that can be considered both genuinely high-dimensional and genuine multiparticle entangled. We consider a natural quantity that characterizes this key property. To detect it, we develop three different classes of criteria. These enable us both to probe the ultimate noise tolerance of this form of entanglement and to make detection schemes using sparse or even minimal measurement resources. The approach provides a simple way of benchmarking entanglement dimensionality in the multiparticle regime and general, platform-independent, detection methods that readily apply to experimental use.

Siping Liu

Quantum entanglement and entanglement measure play an important role in quantum communication theory.In this paper,using a computable measure of entanglement——Negativity,we obtain the Negativity for a two-parameter class of state in high-dimension two-party quantum system.The advantages of this method include its simple evaluation and explicit physic meaning.

Guillaume Aubrun, Szarek, Stanisław