CMSC 491: Introduction to Quantum Computation

In the past two lectures, we have discussed measurements and entanglement. We now combine these two topics to discuss one of the most fundamental questions in quantum theory: Does entanglement as we understand it actually exist in Nature? Recall that in 1935, Einstein, Podolsky and Rosen (EPR) argued that quantum mechanics could not be a complete physical theory due to its prediction of states such as the Bell state |Φ+〉 = 1 √ 2 (|00〉 + |11〉). For example, as we will discuss shortly, the Bell state appears to allow superluminal (i.e. faster than the speed of light) communication, which is impossible by the theory of relativity. Thus, EPR suggested that there must be more to Nature than what quantum theory prescribes — namely, that there must be “ hidden variables” which contain extra information missing in quantum mechanics about what is actually happening in the subatomic world. In other words, the moon is there even if you do not look at it — it’s just that we “do not have access” to the hidden variables prescribing the state of the moon. Moreover, this information must be “local”, in the sense that instantaneous communication between variables should not be possible. Such theories are hence called local hidden variable theories. Remarkably, in 1964, John Bell proved that no local hidden variable theory could ever reproduce the statistics predicted by quantum mechanics! Thus, either local hidden variables theories are wrong, or quantum mechanics is wrong. In fact, Bell went a step further — he proposed a “simple” experiment which could be run in a lab to test which of these two cases represents reality. This experiment was based on (what is now called) a Bell inequality, and was run for example by the celebrated effort of Aspect, Grangier, and Roger in 1981, who wrote about their findings: