Getting more out of every quantum measurement
Most quantum sensing asks how precisely a quantum probe can measure a known quantity, such as a field, a phase or a time interval. Our group approaches the subject from the side of measurement itself. We ask what can be learned from a quantum system while disturbing it as little as possible, with as few changes to the apparatus as possible, and about quantities that a standard measurement cannot access at all.
This has led to:
Alongside these photonic experiments, we work with theory collaborators on using massive objects in spatial superposition to test whether the interactions between them are themselves quantum.
A weak measurement couples a quantum system so gently to a measuring pointer that the system is barely disturbed. Combined with post-selection on a chosen final outcome, it yields a weak value, which can be a complex number or lie outside the usual range of results. We showed that the average of a non-Hermitian operator equals a weak value multiplied by a calculable factor; such operators include those that add or remove a quantum of light, or describe how noise acts on a state. We then showed that such weak values can be read from an interference pattern, with no weak coupling and no post-selection. Where weak values become very large, a conventional weak measurement is limited by how gentle its coupling can be made in practice; in our comparison it could not recover the operator's average in that regime, whereas the interferometric method, which reads the average directly from the fringe contrast, remained accurate.
We placed weakly coupled pointers in both arms of an interferometer, acting on the same heralded single photons in the same run. One pointer registered the photons' presence in one arm; the other registered their diagonal polarization in the other arm. This realised the quantum Cheshire cat effect with genuine weak measurements for the first time, to our knowledge. It is a step towards interacting with different properties of one quantum system in separate locations while disturbing it minimally.
Identifying an unknown quantum state normally means measuring it in several different ways and reconstructing it afterwards. Quantum state interferography does this from one interference pattern recorded without changing any setting. The position, average brightness and contrast of the fringes together fix a qubit's state. We demonstrated the method on the polarization of laser light, with average fidelity above 98% assuming pure input states. We also proposed an extension to higher-dimensional systems that needs only d − 1 interference patterns for a d-level pure state.
The same measurement-centred approach extends to quantities that no ordinary measurement at a single moment can reach. With Rafael Sorkin, we built an optical event filter that asks a question about a photon's path through an interferometer and converts it into one detector reading. The photon's polarization serves as a built-in marker. The quantum measure obtained for that path event was 1.172, above the classical ceiling of one.
→ Read more on Quantum Fundamentals & QIPA massive spatial qubit uses two separated positions of a nano-object as the 0 and 1 of a qubit. Measuring the object's position after different durations of free evolution reads out that qubit in all three bases. With collaborators at UCL, Groningen and the Bose Institute, we have shown how this approach can certify entanglement created by the Casimir interaction between two neutral nano-objects. Such entanglement would show that the interaction is inherently quantum. We have extended the approach to witnessing whether gravity is quantum in nature.
A Mach–Zehnder interferometer with a polariser in one arm and a wave plate in the other, using 810 nm laser light. The weak value inferred from the fringe contrast was 0.501 ± 0.005, against a predicted 0.5. The same quantity was also measured by conventional weak measurement, using a calcite beam displacer, for direct comparison. Where the weak value became very large, that method could not recover the operator's average, because the beam displacement and the extinction ratios of the polarisation optics are finite; the interferometric method remained accurate there.
Suggested figures: Figs. 8 and 11 of the paper, side by side (interferometric vs conventional).A displaced Sagnac interferometer, chosen for its stability against vibration, with He–Ne laser light. Polarization states across the Bloch sphere were reconstructed from single interferograms, with average fidelity above 98% assuming pure states. Reconstructions that also estimated the state's purity had lower fidelity, because imperfections in the setup reduced the fringe contrast.
Suggested figure: Fig. 4 of the paper (fidelity maps on the Bloch sphere).Photon pairs, with one photon heralding its partner, ensured that almost always only one photon was inside the interferometer. Pointer shifts of about 50 µm in both arms gave weak values of 1.08 ± 0.13 for presence and 0.89 ± 0.09 for polarization, against an ideal value of 1.
Suggested figure: Fig. 3 of the paper (open access under CC BY; reuse with attribution).A new graphic and content on quantum imaging with entangled photons are on the way.
