Associated with non-deterministic gates remains high.

An alternative approach is to interact photons deter-

Ministically via an atom-cavity system11,37,38, which

can be con fi gured to implement arbitrary determinis-

Tic interactions39,40 (semiconductor approaches are dis-

cussed below). However, there may be a payo ff between

Resource overhead and susceptibility to errors. What-

Ever the approach to implementing gates, the realisa-

tion of multiple high- fi delity deterministic single-photon

Sources remains a major challenge. In the demonstra-

Tions described above, single photons were generated via

The process of spontaneous parametric downconversion

(SPDC): a bright ‘pump’ laser is shone into a non-linear

Crystal, aligned such that a single pump photon can spon-

Taneously split into two “daughter” photons, conserving

Momentum and energy. Multiplexing several (waveg-

Uide) SPDC sources41 could provide an ideal photon

Source, or single atom or atom-like emitters, such as the

Semiconductor quantum dots described below, could be

Used. The latter shows potential for emitting a string of

Photons pre-entangled in a cluster state42, and as nodes

In quantum networks.

Quantum metrology and lithography

All science and technology is founded on measurement.

Improvements in precision have led not just to more de-

Tailed knowledge but also new fundamental understand-

Ing. This quest to realize ever more precise measurements

Raises the question are there fundamental limits. Since

A measurement is a physical process one may expect the

Laws of physics to enforce such limits. This is indeed the

Case, and it turns out that explicitly quantum mechanical

Systems are required to reach these limits3.

The subwavelength precision o ff ered by optical phase φ

measurements in an interferometer (Fig. 2d) is the rea-

son that they have found applications across all fi elds of

Science and technology, from cosmology (gravity wave de-

Tection) to nanotechnology (phase-contrast microscopy).

Despite this great sensitivity, there is a limit: For a fi nite

Resource (energy, number of photons, etc.) the phase

Sensitivity is limited by statistical uncertainty. It has

Been shown that using semi-classical probes (eg. coher-

ent laser light) limits the sensitivity ∆ φ to the standard

quantum limit (SQL): ∆ φ ∼ 1/√N, where Nis the aver-

Age number of photons used43–45. The more fundamental

Heisenberg limit is attainable with the use of a quantum

probe (eg. an entangled state of photons): ∆ φ ∼ 1/N

(Refs. 3,45)—quantum metrology.

The Heisenberg limit and the SQL can be illustrated

with reference to an interferometer (Fig. 2d), where

We represent a single photon in mode aand no pho-

tons in mode bby the quantum state |10iab. After

the fi rst beam splitter this photon is in a quantum me-

Chanical superposition of being in both paths of the in-

terferometer: (|10icd +|01icd)/√2. After the φ phase

Shift in mode d, this superposition evolves to the state

(|10icd +ei φ |01icd)/√2. After recombining at the second

Beam splitter, the probability of detecting the single pho-

ton in mode eis Pe= (1 −sin φ)/2 (this is just classical

Interference at the single photon level). Determination of

Pecan therefore be used to estimate an unknown phase

shift φ. If we repeat this experiment Ntimes then the un-

certainty in this estimate is ∆ φ ∼ 1/√N—the SQL, aris-

Ing from a Poissonian statistical distribution (the same

Limit is obtained when a bright laser and intensity detec-

tors are used).

If, instead of using photons one at a time, we were able

4

to prepare the maximally entangled N-photon ‘NOON’

state (|N0icd +|0Nicd)/√2 inside the interferometer, this

state would evolve to (|N0icd +eiN φ |0Nicd)/√2 after the

φ phase shift. From this state we could estimate the

phase with an uncertainty ∆ φ ∼ 1/N—the Heisenberg

limit—an improvement of 1/√Nover the SQL. Beating

The SQL is known as phase super-sensitivity46,47.

Interference experiments using two-48, three-46, and

Four-photon states49,50 have been demonstrated, giving

rise to a detection probability p ∝ sin(N φ). Observation

of such a “ λ /N ” fringe, with a period Ntimes shorter

than a conventional interferometer with wavelength λ

Light, is called phase super-resolution46. However, it has

Been demonstrated that phase super-resolution can be

Observed using only semi-classical resources47. Therefore

observation of λ /N fringes does not guarantee quantum

Enhanced phase sensitivity and precise accounting of re-

Sources is required51.