George C. Knee

When Amplification with Weak Values Fails to Suppress Technical Noise

The application of postselection to a weak quantum measurement leads to the phenomenon of weak values. Expressed in units of the measurement strength, the displacement of a quantum coherent measuring device is ordinarily bounded by the eigenspectrum of the measured observable. Postselection can enable an interference effect that moves the average displacement far outside this range, bringing practical benefits in certain situations. Employing the Fisher information metric, we argue that the amplified displacement offers no fundamental metrological advantage, due to the necessarily reduced probability of success. Our understanding of metrological advantage is the possibility of a lower uncertainty in the estimate of an unknown parameter with a large number of trials. We analyze a situation in which the detector is pixelated with a finite resolution, and in which the detector is afflicted by random displacements: imperfections which degrade the fundamental limits of parameter estimation. Surprisingly, weak-value amplification is no more robust to them than a technique making no use of the amplification effect brought about by a final, postselected measurement.

Quantum sensors based on weak-value amplification cannot overcome decoherence

Sensors that harness exclusively quantum phenomena (such as entanglement) can achieve superior performance compared to those employing only classical principles. Recently, a technique based on postselected, weakly performed measurements has emerged as a method of overcoming technical noise in the detection and estimation of small interaction parameters, particularly in optical systems. The question of which other types of noise may be combated remains open. We here analyze whether the effect can overcome decoherence in a typical field-sensing scenario. Benchmarking a weak, postselected measurement strategy against a strong, direct strategy, we conclude that no advantage is achievable, and that even a small amount of decoherence proves catastrophic to the weak-value amplification technique.

Leggett-Garg inequality violations with a large ensemble of qubits

We investigate how discrete internal degrees of freedom in a quasimacroscopic system affect the violation of the Leggett-Garg inequality, a test of macroscopic realism based on temporal correlation functions. As a specific example, we focus on an ensemble of qubits subject to collective and individual noise. This generic model can describe a range of physical systems, including atoms in cavities, electron or nuclear spins in nitrogen-vacancy (NV) centers in diamond, erbium in Y2SiO5, bismuth impurities in silicon, or arrays of superconducting circuits, to indicate but a few. Such large ensembles are potentially more macroscopic than other systems that have been used so far for testing the Leggett-Garg inequality and open a route toward probing the boundaries of quantum mechanics at macroscopic scales. We find that, because of the nontrivial internal structure of such an ensemble, the behavior of different measurement schemes, under the influence of noise, can be surprising. We discuss which measurement schemes are optimal for flux qubits and NV centers, and some of the technological constraints and difficulties for observing such violations with present-day experiments.

Weak-value amplification: state of play

Abstract Weak values arise in quantum theory when the result of a weak measurement is conditioned on a subsequent strong measurement. The majority of the trials are discarded, leaving only very few successful events. Intriguingly those can display a substantial signal amplification. This raises the question of whether weak values carry potential to improve the performance of quantum sensors, and indeed a number of impressive experimental results suggested this may be the case. By contrast, recent theoretical studies have found the opposite: using weak-values to obtain an amplification generally worsens metrological performance. This survey summarises the implications of those studies, which call for a reappraisal of weak values’ utility and for further work to reconcile theory and experiment.

A hybrid-systems approach to spin squeezing using a highly dissipative ancillary system

Squeezed states of spin systems are an important entangled resource for quantum technologies, particularly quantum metrology and sensing. Here we consider the generation of spin squeezed states by interacting the spins with a dissipative ancillary system. We show that spin squeezing can be generated in this model by two different mechanisms: one-axis twisting and driven collective relaxation. We can interpolate between the two mechanisms by simply adjusting the detuning between the dissipative ancillary system and the spin system. Interestingly, we find that for both mechanisms, ancillary system dissipation need not be considered an imperfection in our model, but plays a positive role in spin squeezing. To assess the feasibility of spin squeezing we consider two different implementations with superconducting circuits. We conclude that it is experimentally feasible to generate a squeezed state of hundreds of spins either by one-axis twisting or by driven collective relaxation.

Towards optimal experimental tests on the reality of the quantum state

The Barrett–Cavalcanti–Lal–Maroney (BCLM) argument stands as the most effective means of demonstrating the reality of the quantum state. Its advantages include being derived from very few assumptions, and a robustness to experimental error. Finding the best way to implement the argument experimentally is an open problem, however, and involves cleverly choosing sets of states and measurements. I show that techniques from convex optimisation theory can be leveraged to numerically search for these sets, which then form a recipe for experiments that allow for the strongest statements about the ontology of the wavefunction to be made. The optimisation approach presented is versatile, efficient and can take account of the finite errors present in any real experiment. I find significantly improved low-cardinality sets which are guaranteed partially optimal for a BCLM test in low Hilbert space dimension. I further show that mixed states can be more optimal than pure states.

Attosecond-resolution Hong-Ou-Mandel interferometry.

A new Hong-Ou-Mandel interferometer protocol achieves few-attosecond (nanometer) photon path delay resolution. When two indistinguishable photons are each incident on separate input ports of a beamsplitter, they “bunch” deterministically, exiting via the same port as a direct consequence of their bosonic nature. This two-photon interference effect has long-held the potential for application in precision measurement of time delays, such as those induced by transparent specimens with unknown thickness profiles. However, the technique has never achieved resolutions significantly better than the few-femtosecond (micrometer) scale other than in a common-path geometry that severely limits applications. We develop the precision of Hong-Ou-Mandel interferometry toward the ultimate limits dictated by statistical estimation theory, achieving few-attosecond (or nanometer path length) scale resolutions in a dual-arm geometry, thus providing access to length scales pertinent to cell biology and monoatomic layer two-dimensional materials.

Projected gradient descent algorithms for quantum state tomography

Accurate quantum tomography is a vital tool in both fundamental and applied quantum science. It is a task that involves processing a noisy measurement record in order to construct a reliable estimate of an unknown quantum state, and is central to quantum computing, metrology and communication. To date, many different approaches to quantum state estimation have been developed, yet no one method fits all applications, and all fail relatively quickly as the dimensionality of the unknown state grows. In this work, we suggest that projected gradient descent is a method that can evade some of these shortcomings. We present three tomography algorithms that use projected gradient descent and compare their performance with state-of-the-art alternatives, i.e., the diluted iterative algorithm and convex programming. Our results find in favour of the general class of projected gradient descent methods due to their speed, applicability to large states, and the range of conditions in which they perform as well as providing insight into which variant of projected gradient descent ought to be used in various measurement scenarios.Quantum science: states that wander find home fasterThe recovery of a quantum state from experimental measurement is a challenging task that often relies on iteratively updating the estimate of the state at hand. Letting quantum state estimates temporarily wander outside of the space of physically possible solutions helps speeding up the process of recovering them. A team led by Jonathan Leach at Heriot-Watt University developed iterative algorithms for quantum state reconstruction based on the idea of projecting unphysical states onto the space of physical ones. The state estimates are updated through steepest descent and projected onto the set of positive matrices. The algorithms converged to the correct state estimates significantly faster than state-of-the-art methods can and behaved especially well in the context of ill-conditioned problems. In particular, this work opens the door to full characterisation of large-scale quantum states.

Optimal Trotterization in universal quantum simulators under faulty control

Universal quantum simulation may provide insights into those many-body systems that cannot be described classically, and that cannot be efficiently simulated with current technology. The Trotter formula, which decomposes a desired unitary time evolution of the simulator into a stroboscopic sequence of repeated elementary evolutions, is a key algorithmic component which makes quantum simulation of dynamics tractable. The Trotter number

Seeing opportunity in every difficulty: protecting information with weak value techniques

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