How Can One Measure Quantum Entanglement

Jennie Sköld

Quantum entanglement is a phenomenon which has shown great potential use in modern technical implementations, but there is still much development needed in the field. One major problem is how to measure the amount of entanglement present in a given entangled state. There are numerous different entanglement measures suggested, all satisfying some conditions being of either operational, or more abstract, mathematical nature. However, in contradiction to what one might expect, the measures show discrepancies in the ordering of entangled states. Concretely this means that with respect to one measure, a state can be more entangled than another state, but the ordering may be opposite for the same states using another measure. In this thesis we take a closer look at some of the most commonly occurring entanglement measures, and find examples of states showing inequivalent entanglement ordering for the different measures.

Leah Henderson

P. K. Aravind

Ethan Dederick, M. Beck

We have performed a series of experiments using a spontaneous parametric down-conversion source to produce pairs of photons in either entangled or non-entangled polarization states. We determine the full quantum mechanical polarization state of one photon, conditioned on the results of measurements performed on the other photon. For non-entangled states, we find that the measured state of one photon is independent of measurements performed on the other. However, for entangled states, the measured state does depend on the results of measurements performed on the other photon. This is possible because of the nonlocal nature of entangled states. These experiments are suitable for an undergraduate teaching laboratory.

Gerardo Adesso, Marco Piani

Chandan Datta, Tanmoy Biswas, Debashis Saha +1 more

Abstract Distinguishing physical processes is one of the fundamental problems in quantum physics. Although distinguishability of quantum preparations and quantum channels have been studied considerably, distinguishability of quantum measurements remains largely unexplored. We investigate the problem of single-shot discrimination of quantum measurements using two strategies, one based on single quantum systems and the other one based on entangled quantum systems. First, we formally define both scenarios. We then construct sets of measurements (including non-projective) in arbitrary finite dimensions that are perfectly distinguishable within the second scenario using quantum entanglement, while not in the one based on single quantum systems. Furthermore, we show that any advantage in measurement discrimination tasks over single systems is a demonstration of Einstein–Podolsky–Rosen ‘quantum steering’. Alongside, we prove that all pure two-qubit entangled states provide an advantage in a measurement discrimination task over one-qubit systems.