When a speaker brings a tangle of garden hoses, a bottle of water, and a towel to the podium, you know it's going to be a fun talk. Computer scientist Harry Buhrman of the Centrum Wiksunde & Informatica in Amsterdam recently visited Singapore to help celebrate the fourth anniversary of the Centre for Quantum Technologies. He and his props gave quantum cryptography a whole new dimension--literally. Instead of encrypting a message or authenticating someone's identity, Buhrman posed a deceptively simple question: Can someone be sure you are where you say you are?
Figure 1
Figure 2
Position verification isn't just of interest to spouses who wonder about all those late nights at the office. It would tighten up secure communications channels and make it possible to send Mission Impossible-style messages that could be read only if someone visited a certain location (like geocaching puzzles). For fundamental physicists, the procedure raises an important question about the operational meaning of space. If you cannot confirm, even in principle, whether something is at a given location, does the concept of location have any objective meaning? In fact, the scenario Buhrman laid out bore a spooky resemblance to the holographic principle in quantum gravity.
Imagine trying to confirm your position in one dimension, along a straight line (Figure 1). A verifier can use the procedure of Einstein synchronization: send you a signal, to which you reply, and measure the round-trip time in order to gauge the distance between the two of you. It is the maximum distance; you might be closer, given the delays that could arise in the process. To narrow down your location, a second verifier on the opposite side of you also sends a signal that you must reply to. This technique goes by the name of distance bounding.
It's easy to game the system, however (Figure 2). Two comrades intercept the signals, wait a short while (to simulate the travel time to your purported position), and reply on your behalf. Now you don't need to be where you claim to be. With your friends covering for you, you can safely leave the office and have your affair.
(Images courtesy of Harry Buhrman.)
More nefarious scheming in the second part of this post, where things get quantum...