Quantifying Coherence and Entanglement via a Simple Measurement

Neha Pathania, Tabish Qureshi

Graeme Smith, John A. Smolin, Xiao Yuan +3 more

Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction of the system state. We show that one can extract quantitative bounds to the relative entropy of coherence and the coherent information, coherence and entanglement quantifiers respectively, by a limited number of purity measurements. The scheme is readily implementable with current technology to verify quantum computations in large scale registers, without carrying out expensive state tomography.

Mohd Shoaib Qureshi, Tabish Qureshi

Quantum decoherence refers to the phenomenon when the interaction of a quantum system with its environment results in the degradation of quantum coherence. Decoherence is considered to be the most popular mechanism responsible for the emergence of classicality from quantum mechanics. The issue of formulating a measure of decoherence is addressed here. The approach taken here is that decoherence results from the entanglement of a quantum system with certain environment degrees of freedom, and quantifying this entanglement should yield the most natural measure of decoherence. A simple measure of decoherence is presented based on this notion, and it is examined for various example systems. The measure proves to be effective and is relatively straightforward to compute. In addition, a method has been proposed to measure decoherence in a Mach-Zehnder interferometer which may be useful in neutron interferometry.

Leah Henderson

Harald Wunderlich, S. Virmani, Martin Bodo Plenio

Quantifying experimentally created entanglement could in principle be accomplished by measuring the entire density matrix and calculating an entanglement measure of choice thereafter. Due to the tensor structure of the Hilbert space, this approach becomes unfeasible even for medium-sized systems. Here we present methods for quantifying the entanglement of arbitrarily large two-colorable graph states from simple measurements. The presented methods provide non-trivial bounds on the entanglement for any state as long as there is sufficient fidelity with such a graph state. The measurement data considered here is merely given by stabilizer measurements, thus leading to an exponential reduction in the number of measurements required. We provide analytical results for the robustness of entanglement and the relative entropy of entanglement.

Lian-Wu Yang, Zhong‐Xiao Man, Yun‐Jie Xia +1 more