Abstract
Twenty-five years after the invention of quantum teleportation, the concept of entanglement gained enormous popularity. This is especially nice to those who remember that entanglement was not even taught at universities until the 1990s. Today, entanglement is often presented as a resource, the resource of quantum information science and technology. However, entanglement is exploited twice in quantum teleportation. Firstly, entanglement is the “quantum teleportation channel”, i.e., entanglement between distant systems. Second, entanglement appears in the eigenvectors of the joint measurement that Alice, the sender, has to perform jointly on the quantum state to be teleported and her half of the “quantum teleportation channel”, i.e., entanglement enabling entirely new kinds of quantum measurements. I emphasize how poorly this second kind of entanglement is understood. In particular, I use quantum networks in which each party connected to several nodes performs a joint measurement to illustrate that the quantumness of such joint measurements remains elusive, escaping today’s available tools to detect and quantify it.
Highlights
In 1993 six co-authors surprised the world by proposing a method to teleport a quantum state from one location to a distant one [1,2]
The joint measurement exploited in quantum teleportation, known as a Bell state measurement (BSM), is characterized by all its eigenvectors being maximally entangled
If Alice, Bob and Charlie each perform the BSM, there is a simple classical model that reproduces the statistics of their outcomes, p( a, b, c)—notice that there are no inputs
Summary
In 1993 six co-authors surprised the world by proposing a method to teleport a quantum state from one location to a distant one [1,2]. Entanglement appears a second time in quantum teleportation: the measurement that Alice has to perform jointly on the quantum state to be teleported and her half of the “quantum teleportation channel” has all its eigenstates maximally entangled. The two systems can answer “yes” and get (maximally) entangled in such a way that whatever identical questions are later asked to them, they’ll provide the same answer. The answer could be “no” and the two systems get into a different (maximally) entangled state such that their answer to arbitrary but identical questions would always be opposite. Physics requires an understanding of such joint measurements of similar quality as our understanding of entanglement between distant systems, i.e., of entanglement as quantum teleportation channels.
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