Geoff J. Pryde

Entanglement-free Heisenberg-limited phase estimation

Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific discoveries. At the fundamental level, measurement precision is limited by the number N of quantum resources (such as photons) that are used. Standard measurement schemes, using each resource independently, lead to a phase uncertainty that scales as 1/—known as the standard quantum limit. However, it has long been conjectured that it should be possible to achieve a precision limited only by the Heisenberg uncertainty principle, dramatically improving the scaling to 1/N (ref. 3). It is commonly thought that achieving this improvement requires the use of exotic quantum entangled states, such as the NOON state. These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N ≤ 6 (refs 6–15), but few have surpassed the standard quantum limit and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure. We replace entangled input states with multiple applications of the phase shift on unentangled single-photon states. We generalize Kitaev’s phase estimation algorithm using adaptive measurement theory to achieve a standard deviation scaling at the Heisenberg limit. For the largest number of resources used (N = 378), we estimate an unknown phase with a variance more than 10 dB below the standard quantum limit; achieving this variance would require more than 4,000 resources using standard interferometry. Our results represent a drastic reduction in the complexity of achieving quantum-enhanced measurement precision.

Quantum Process Tomography of a Controlled-NOT Gate

We demonstrate complete characterization of a two-qubit entangling process--a linear optics controlled-NOT gate operating with coincident detection--by quantum process tomography. We use a maximum-likelihood estimation to convert the experimental data into a physical process matrix. The process matrix allows an accurate prediction of the operation of the gate for arbitrary input states and a calculation of gate performance measures such as the average gate fidelity, average purity, and entangling capability of our gate, which are 0.90, 0.83, and 0.73, respectively.

Experimental EPR-steering using Bell-local states

Erwin Schrodinger introduced in 1935 the concept of ‘steering’, which generalizes the famed Einstein–Podolsky–Rosen paradox. Steering sits in between quantum entanglement and non-locality — that is, entanglement is necessary for steering, but steering can be achieved, as has now been demonstrated experimentally, with states that cannot violate a Bell inequality (and therefore non-locality).

Measurement of Quantum Weak Values of Photon Polarization

We experimentally determine weak values for a single photon’s polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave theory, due to the two-photon entanglement. We observe the variation in the size of the weak value with measurement strength, obtaining an average measurement of the S1 Stokes parameter more than an order of magnitude outside of the operator’s spectrum for the smallest measurement strengths.

Time-Reversal and Super-Resolving Phase Measurements

We demonstrate phase super-resolution in the absence of entangled states. The key insight is to use the inherent time-reversal symmetry of quantum mechanics: our theory shows that it is possible to measure, as opposed to prepare, entangled states. Our approach is robust, requiring only photons that exhibit classical interference: we experimentally demonstrate high-visibility phase super-resolution with three, four, and six photons using a standard laser and photon counters. Our six-photon experiment demonstrates the best phase super-resolution yet reported with high visibility and resolution.

Heralded noiseless linear amplification and distillation of entanglement

A noiseless linear amplifier for quantum states of an optical field is demonstrated. The amplifier is also used to enhance entanglement through a technique known as distillation. Such amplification and distillation may be useful for quantum cloning, metrology and communications.

Violation of the Leggett–Garg inequality with weak measurements of photons

By weakly measuring the polarization of a photon between two strong polarization measurements, we experimentally investigate the correlation between the appearance of anomalous values in quantum weak measurements and the violation of realism and nonintrusiveness of measurements. A quantitative formulation of the latter concept is expressed in terms of a Leggett–Garg inequality for the outcomes of subsequent measurements of an individual quantum system. We experimentally violate the Leggett–Garg inequality for several measurement strengths. Furthermore, we experimentally demonstrate that there is a one-to-one correlation between achieving strange weak values and violating the Leggett–Garg inequality.

Entanglement-enhanced measurement of a completely unknown optical phase

We demonstrate a method for achieving phase measurements with accuracy beyond the standard quantum limit using entangled states. A sophisticated feedback scheme means that no initial estimate of the phase is required.

Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole

Demonstrating nonclassical effects over longer and longer distances is essential for both quantum technology and fundamental science. The main challenge is the loss of photons during propagation, because considering only those cases where photons are detected opens a ‘‘detection loophole’’ in security whenever parties or devices are untrusted. Einstein-Podolsky-Rosen steering is equivalent to an entanglement-verification task in which one party (device) is untrusted. We derive arbitrarily loss-tolerant tests, enabling us to perform a detection-loophole-free demonstration of Einstein-Podolsky-Rosen steering with parties separated by a coiled 1-km-long optical fiber, with a total loss of 8.9 dB (87%).

Measuring a Photonic Qubit without Destroying It

Measuring the polarization of a single photon typically results in its destruction. We propose, demonstrate, and completely characterize a quantum nondemolition (QND) scheme for realizing such a measurement nondestructively. This scheme uses only linear optics and photodetection of ancillary modes to induce a strong nonlinearity at the single-photon level, nondeterministically. We vary this QND measurement continuously into the weak regime and use it to perform a nondestructive test of complementarity in quantum mechanics. Our scheme realizes the most advanced general measurement of a qubit to date: it is nondestructive, can be made in any basis, and with arbitrary strength.