Illustrated Physics
physics, drawn
Concept

Qubit — where it appears

A quantum system with two distinguishable states that can be held in any superposition of them, used as the unit of quantum information. It can be an atom, an ion, a photon's polarisation or a superconducting circuit, and its worth is set by how long the superposition survives.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

A pendulum with unequal steps. The potential −EJ cos φ of the junction against its phase, at EJ/EC = 50, with the lowest 4 levels of the circuit drawn across the well between their classical turning points, in units of the charging energy. The transitions are 18.94, 17.79, 16.50, each smaller than the one below it; a harmonic well of the same curvature would space them all at the square root of 8·EJ·EC, 20.00. The spacing shrinks because the cosine is flatter than a parabola away from its bottom, and the shrinking is what lets a microwave pulse tuned to the lowest transition leave the next one alone.

The circuit that forgets its charge

A tiny superconducting island joined to its surroundings through a Josephson junction has discrete energy levels, and two of them make a quantum bit. The first such circuits were ruined by stray charges on nearby surfaces, which moved their levels and scrambled any superposition within a nanosecond. The cure was to make the junction's energy fifty times the charging energy. That makes the levels exponentially insensitive to charge while costing only a power-law loss in the unequal spacing that lets one transition be driven alone.

electromagnetism · Superconductivity A temperature the circuit refuses to go below. The escape temperature — the temperature that would give the measured escape rate if escape were purely thermal — against the actual temperature of the junction, for a 10 µA, 5 pF junction at biases of 0.985 and 0.99 of its critical current. Hot, the two are equal: the phase is kicked over the barrier by thermal noise. Cooled below the crossover, 39 mK at 0.985 and 36 mK at 0.99, the escape temperature stops falling and levels off at 42 mK and 44 mK: the rate no longer depends on the temperature at all. This levelling-off, measured by Michel Devoret, John Martinis and John Clarke in 1985 with the junction's electrical environment carefully characterised, was the evidence that a macroscopic electrical variable tunnels.

The circuit that goes through a wall

Tunnelling is usually told about electrons and alpha particles — single, small, quantum things passing through barriers they cannot climb. In 1985 it was seen in an electrical circuit: the phase difference across a Josephson junction, a coordinate shared by all the electrons in two pieces of superconducting metal, trapped in a well and escaping from it through the barrier rather than over it. The evidence was a temperature below which the circuit's escape rate stopped caring how cold it was. The same circuit showed discrete energy levels, and its descendants are the qubits of superconducting quantum computers.

quantum · Tunnelling Four operations on one half, four states of the pair. The sender holds one half of an entangled pair prepared in the state |Φ+⟩ = (|00⟩ + |11⟩)/√2, the receiver the other. To send two bits she applies one of four operations to her half alone — do nothing, flip it (X), shift its phase (Z), or both — and sends it. The table gives, computed from the state vectors, the probability that the receiver's joint measurement of both halves in the Bell basis returns each of the four Bell states: one on the diagonal, zero everywhere else. Four perfectly distinguishable outcomes from one transmitted qubit is two bits. Sent without the pair, a qubit can carry at most one.

The qubit that carries two bits

A single quantum two-state system, sent from one person to another, can carry at most one bit of message — a theorem, not an engineering limit. If the two already share half each of an entangled pair, the sender can do one of four things to her half alone, send just that half, and the receiver can tell which of the four she did. Two bits arrive on one qubit. Nothing is free: the shared pair had to be delivered, and counted honestly the rate is still a bit per qubit. What entanglement buys is the freedom to send half the message before the message exists, and it also buys privacy, since the qubit in transit carries nothing at all on its own.

quantum · Entanglement Two measures of how uncertain a split state is. For the two-peaked state, against half the separation of the peaks in units of their width: Heisenberg's product σₓσₚ divided by its minimum ħ/2 (solid), and the entropic sum Hₓ + Hₚ minus its minimum ln(πeħ) (dashed), both computed from the state's distributions. As the peaks separate the product grows without limit, 8.1 times the minimum at the right of the figure, because the variance counts the empty space between the peaks as uncertainty. The entropic excess levels off at 2 ln 2 − 1 = 0.386 (0.386 at the right): the position's entropy gains ln 2, one bit, for not knowing which peak, and the momentum's gives back 1 − ln 2 because its fringes pack it into narrow bands. The entropic relation says what is true of the state: it is a fraction of a coin toss away from a minimum-uncertainty packet, however far apart the two places are.

The sharpness a variance cannot see

Heisenberg's inequality is a statement about standard deviations, and a standard deviation is a poor measure of how sharply something is known. A particle that is certainly in one of two narrow places a metre apart has a position spread of half a metre, and satisfies the inequality with room to spare while being sharply localised. Measure uncertainty by information instead — by the Shannon entropy of each distribution — and the relation tightens: the sum of the two entropies has a floor that the split state cannot get under either, and the floor survives in places where the variance form says nothing at all.

quantum · Uncertainty

Named alongside it

The objects these essays reach for when they reach for this one.

DecoherenceTunnellingAngular momentumAnharmonicityBell stateCharge dispersionCharging energyCooper-pairDissipationEntanglementEntropyFourier transform

All concepts