Why Nobody Understands Quantum Physics: The bestselling guide to our universe

by Frank Verstraete

First the bad news. The entanglement patterns of quantum many-particle systems open up an entirely new world of applications for processing and transmitting information, theoretically in an exponentially much more efficient way than is possible with classical systems. So far so good. But there’s a catch that tempers this optimism: a system of n qubits can only store n classical bits of information. This limitation is also known as the ‘Holevo bound’, named after Alexander Holevo (b. 1943).

Conclusion: it’s not possible for a quantum system to store exponentially large amounts of classical information. As soon as you observe the quantum system (or, in this analogy, read one page of the encyclopaedia), the rest of the information is irretrievably lost.

According to Heisenberg’s uncertainty principle, an eavesdropper cannot intercept any information unless they know the correct base. This makes it impossible for them to copy the qubits in transit, a limitation known as the no-cloning theorem. You can’t measure (or steal, or ‘borrow’) quantum information without disrupting it (i.e. breaking the superposition). If someone tries to do so, errors will inevitably creep into the communication.

A quantum computer becomes truly advantageous when the total number of 1- and 2-qubit operations required to solve a problem is exponentially smaller than the number of operations needed for a classical computer to perform the same task.

Why the fuss? Because many, not entirely incomprehensibly, were daunted by two major and seemingly insurmountable obstacles. First of all: quantum computers operate in the exponentially large Hilbert space, consisting of an equally exponential number of energy levels. Surely, sceptics argued, such a machine would require an exponentially precise control system, composed of utterly utopic lasers. And then came the other problem: decoherence. This merciless phenomenon reduces entangled quantum states to classical states due to interaction with the environment.