THE QUANTUM INTELLIGENCER

A general framework for certifying quantum memories has been presented, together with a demonstration on a solid-state quantum memory, which it certified at an average channel fidelity of 98.6 percent. The framework draws on the theory of quantum channels, treating a memory as a channel whose performance may be quantified, and estimates the average channel fidelity experimentally through a finite set of probe states arranged as a so-called 2-design. The authors further show that this single quantity gives access to other properties of the channel, including its dimensionality and its capacity to transmit quantum information, and they consider prepare-and-measure, entanglement-based and semi-device-independent settings for the certification. The methods, they observe, may be applied as readily to fibres, transducers and gates as to memories themselves. For a reader unfamiliar with the field, three terms carry the weight of the result. A quantum memory is a device whose business is to receive a quantum state, keep it for an interval, and yield it up again. The keeping is the difficulty. Unlike a page or a ledger, a quantum state cannot be copied for safety, and any commerce with the surrounding world, any reading, any stray warmth, tends to disturb what is held. A memory is therefore judged by fidelity: the measure of how closely what comes out resembles what went in. The authors do not ask whether a memory is perfect, which would be a question with a short answer, but how faithful it is, and they express the answer as a number between zero and one, or as a percentage. The term average channel fidelity is best taken in two parts. A channel is the general name for any process that takes a quantum state at one end and delivers a quantum state, changed or unchanged, at the other: a wire, a lens, a delay. Regarded so, a memory is a channel whose particular work is delay. Fidelity measures the agreement between output and input, and the word average records that the measurement is not taken on one ideal state but across a designed set of probes. That designed set of probes is the 2-design. It would be a large labour to test a memory against every possible state it might be asked to hold. The authors use a finite collection of probe states chosen so that, for the purposes of such averages, they stand faithfully for the whole; the statistical behaviour of the collection matches that of the entire space. This is the economy that makes certification possible in a finite experiment. Of dates, the paper gives none; of trial counts, none. The supporting construction, the 2-design, is described by its averaging property rather than by the number of probe states it contains. No date of measurement is attached to the certified result, and no count of experiments accompanies it. What the paper presents is a single metric, the average channel fidelity, together with the method for obtaining it; the metric's role in this account is to stand as the demonstration rather than to open a longer statistical ledger. Set the abstraction aside and take the demonstration itself. Somewhere in the experimenters' laboratory, a solid-state memory was asked to perform the one task a memory exists to perform: to receive a quantum state, hold it, and give it back. The certification did not ask whether the giving back was perfect. It asked how close the return was to the original, and expressed the answer as a number. That number, averaged over the finite set of probe states, was 98.6 percent. Rendered in plainer proportion, the state that emerged from the memory agreed with the state that entered to the extent of 986 parts in a thousand; the remaining fourteen parts are the measure of how far the returned state falls short of the sent one. That shortfall is not carelessness in the device but the cost of the keeping: the disturbance a state suffers merely by being held in matter. To see why this counts as a practical instance rather than a curiosity, consider what the alternative would be. Without such a number, a memory is an object of hope; with it, a memory becomes an object of account. The same method, the authors observe, may be applied to fibres, transducers and gates, the other things through which a quantum state must pass. The solid-state memory is simply the first ledger entry in a book that stands ready to receive the rest. —Dr. Octavia Blythe Dispatch from The Prepared E0