# Quantum Information Science news

## Our work on the cover of PRL

In a work appearing on the cover of Physical Review Letters, volume 125, issue 8, we with collaborators at the University of Nanjing, China and the University of Ottawa, Canada, have shown that even noisy and saturating detectors can approach shot-noise-limited detection if used judiciously. Shot-noise-limited optical detection is the first, and often the most challenging, step to quantum-enhanced optical sensing. This work uses a technique called weak-value amplification and enables, over a range of input light intensity well beyond the dynamic range of the photodetector, shot-noise-limited detection. Weak-value amplification relies on the principle that only a subset of the photons contains almost all of the information about the sensed object.

## Accreditation protocol published in New Journal of Physics

As the first generation of quantum computers are now reaching the point where they can answer such otherwise impossible questions, it is necessary to consider how the answers of these early devices can be confirmed correct. The full power of quantum computing includes a wide range of problems for which this is not possible, instead demanding new techniques to test quantum computers. A new test has now been proposed by Samuele, Theodoros, and Animesh which can be used to make sure the quantum computer is working correctly without using excessive additional resources while still testing the entire quantum computer. Published in the New Journal of Physics (DOI:10.1088/1367-2630/ab4fd6), this protocol uses circuits which have the same form as the desired circuit but are formulated to give known outcomes. Based on the accuracy of these circuits they are able to place a statistical bound on how close the distribution the quantum computer gives is to the correct distribution.

## Paper on evaluating fundamental sensitivity limits in Physical Review Letters

Francesco, Jamie, and Animesh have published new work in Physical Review Letters which demonstrates that the Holevo Cramér-Rao bound, the fundamental limit to how precise any sensor can be, can be evaluated by numerically efficient methods. Computation of the Holevo Cramér-Rao bound requires the solving of a non-linear optimisation problem. In this publication Francesco, Jamie, and Animesh demonstrate that the necessary optimisation can be expressed as a convex optimisation problem. This realisation allows efficient numerical evaluation of the Holevo Cramér-Rao bound, opening up the possibility of practically applying it in quantum sensing problems.

## Metrology papers published in Physical Review A

Two metrology papers from the group have recently been published in Physical Review A.

## Theo and Animesh publish quantum verification paper in Quantum

Theodoros and Animesh have published a work which sets out a method to verify quantum computational supremacy in near-future quantum devices. This work published in Quantum (DOI:10.22331/q-2019-07-12-164) introduces a verification scheme for an Ising sampler, which if implemented could prove quantum computational supremacy.

## Covert sensing paper published in PRA

Sensing has been in the centre of interest of the quantum information community in the last years. The main reason is that quantum mechanics allow for enhanced precision and the foremost focus has been to find optimal quantum probe states and measurements to attain the quantum enhanced precision.

In their recent work (DOI: 10.1103/PhysRevA.99.062321), Christos (Arizona, formerly at Warwick), Animesh, and colleagues from the University of Arizona, unlock another kind of feature: active covert sensing. The key element of covert sensing is that the sensing light can be hidden in the thermal environment. Specifically, it is shown that it is possible to sense a phase while an adversary remains unaware of the sensing process and they give the fundamental limit: The mean square error of any covert sensing task is lower bounded by the inverse square root of the probe's number of modes (or the number sensing attempts). Any attempt of the sensor to improve the precision necessarily leads to detection by the adversary

## Quantum errors paper published in PRA

Quantum computing is entering a new era of remotely-accessible quantum machines and, given their recent development, computation is more than likely accompanied by errors. One such error—quantum leakage—is an often-overlooked imperfection that amounts to quantum information escaping from the desired computational space and whose presence is rarely identified by a remote user. In work published in Physical Review A (DOI:https://doi.org/10.1103/PhysRevA.99.032328) Armands, Animesh, and George adapt one of dimension witness protocols designed for the purpose of a remote discovery of leakage and equip it with statistically robust, user-defined confidence levels before applying to a remotely accessed quantum processor. They find a circuit component "transmon" acting in a higher computational space than advertised.

## Quantum coherence paper published in PRA

Published this week in the journal *Physical Review A*, the paper "Subtleties of witnessing quantum coherence in nonisolated systems" (DOI: 10.1103/PhysRevA.98.052328) from George, Max, Luke, and Animesh could lead to experiments that help solve the debate on whether biological processes exploit quantum mechanics to their advantage, and whether evolution could provide us with a template for quantum technologies such as computers, sensors and energy sources.

## Quantum metrology paper published in PRL

Working in collaboration with Haixing Miao (University of Birmingham), Dominic and Animesh have published a paper on the fundamental quantum limits of optomechanical sensors in Physical Review Letters (DOI: 10.1103/PhysRevLett.121.110505). Being able to measure very weak forces is central to many applications, such as the direct detection of gravitational waves and monitoring subterranean movement of magma in volancially-active areas. The strength of a force can be inferred through its effect of displacing a mass: the displacement can be sensed by illuminating it with a laser and observing the reflected light, a case of optomechanical sensing. In this work, Dominic, Haixing and Animesh study the best precision attainable by optomechanical sensors when multi-coloured light is used.

## Quantum verification paper published in PRA

Samuele, Theodoros, and Animesh have published a paper on verification in Physical Review A (DOI: https://doi.org/10.1103/PhysRevA.98.022323) demonstrating an improvement on the existing requirements for schemes to verify quantum computations. Quantum computers are capable of solving certain problems whose scale lies outside that of classical computers. For some of these problems not even the solution can be efficiently checked with a classical computer. While schemes can verify an arbitrary quantum computation with a limited set of quantum operations, the minimum quantum resources to perform such a verification is an open question. In this work authors from the group demonstrate a verification scheme which works with a further reduced number of such quantum operations.

## Theodoros publishes review on quantum verification

Working with former Edinburgh colleagues Alexandru Gheorghiu and Elham Kashefi, Theodoros has published a review paper exploring existing techniques for the verification of quantum computation (DOI:10.1007/s00224-018-9872-3) in Theory of Computation.

Quantum computers offer the prospect of solving computational problems which would take an infeasible amount of time to solve with classical devices. For some of these, the solutions cannot be checked without solving the problem again - which would require use of and trust in a quantum computer. Through quantum verification techniques it becomes possible to test the performance of a quantum computer and even test whether a claimed quantum computer is genuine.

Along with an overview of the fundamental obstacle, a number of schemes which allow verification if the user has access to basic quantum apparatus, which allows them to confidently prepare a handful of simple states or to perform a few simple measurements, are discussed and compared in the review paper.

## George publishes in Science Advances

Working in collaboration with experimentalists at Heriot-Watt and Glasgow Universities, the paper entitled Attosecond-resolution Hong-Ou-Mandel interferometry (DOI:10.1126/sciadv.aap9416) has been published in Science Advances.

The team investigated an optical sensor that uses a type of interferometry based on the Hong-Ou-Mandel effect, whereby two identical photons deterministically bunch together at a balanced beam splitter. They were able to measure the optical thickness of an object by looking at the change in coincidence rate of a pair of photodetectors placed at the output of the beam splitter.

## George's work recognised by NJP

The New Journal of Physics has selected George Knee's paper "Towards optimal experimental tests on the reality of the quantum state" (DOI:10.1088/1367-2630/aa54ab) as one of their Highlights of 2017, recognising high-quality publications which have been well-received by the community.

The paper, which looks to find tests demonstrating the reality of the quantum state with ever stronger certainty, is one of just six quantum physics papers published in NJP last year to receive such recognition in the NJP's Highlights of 2017.

## Paper selected for Editor's Suggestions in Phys. Rev. Letts.

A recent PRL on quantum metrology (DOI: 10.1103/PhysRevLett.119.130504), written by Animesh and external collaborators, has been selected as an Editor's Suggestion. The quantum Cramér-Rao bound is a lower bound on the attainable precision when estimating unknown properties of or parameters encoded in a quantum state. When estimating multiple parameters, it is not necessarily physically possible to construct an experiment capable of reaching the precision given by the quantum Cramér-Rao bound. In the letter they discuss the existence of a measurement which can be used to reach the precision of the quantum Cramér-Rao bound. Focusing on pure states being used to estimate a set of phases, a number of necessary and sufficient conditions are derived which projective measurements must satisfy in order to obtain the best possible precision.

## Publication in Linear Algebra and Its Applications

In collaboration with David Simmons and Justin Coon from Oxford Engineering, Animesh has had a paper published in Linear Algebra and Its Applications (DOI: 10.1016/j.laa.2017.06.038) which explores the relationship between the symmetric Laplacian of a graph (an extension of the graph Laplacian to irregular graphs) and the partial trace of an entangled pure state which can be associated with that graph. They show that the Von Neumann entropy of the graph can be a measure of bipartite entanglement in the corresponding pure state and explore the Renyi entropies of various graphs; demonstrating that the complete graph attains maximum entropy and showing extremal values for the k-regular and star graphs which contrasts with results obtained from analysing the ordinary graph Laplacians.

## Quantum metrology paper in Quantum Science and Technology

Magda, Tillmann, and Animesh have had a paper accepted into Quantum Science and Technology (https://iopscience.iop.org/article/10.1088/2058-9565/aa7fa9) which looks at the trade-offs faced when attempting to simultaneously estimate phase and phase diffusion. Looking at states which have a fixed total number of particles they have shown that a fixed number state can attain the maximum possible trade-off in the limit of large phase diffusion. In the case of small phase diffusion they specifically considered Holland-Burnett states, which are derived from inputting a fixed number of photons into each input port of a balanced beam splitter and known to perform well for phase estimation, and found that this was a factor of two below the maximum trade-off possible in the limit that phase diffusion approaches zero.

## Covert quantum sensing work presented at ISIT

Recent work on covert quantum sensing by Christos and Animesh is today being presented at the IEEE International Symposium on Information Theory in Aachen (ISIT 2017) by collaborator Boulat Bash. Typically parameter estimation benefits from the use of high energy probe states which use many photons to obtain a high-precision estimate of an unknown parameter. However such probes can easily be detected by an adversary who can recognise an attempt to probe this system by detecting these probe photons. In order to prevent the target itself or any third-parties from observing an attempt at sensing it is necessary to devise covert methods, hiding the probe state photons among thermal photons from the environment, which restrict the attainable precision. To quantify this restriction, a covertness constraint is derived which imposes a limitation on the probe state energy. While the mean square error scales, in general, with the number of repeated channel uses; these new results show that the improvement cannot exceed the square root of n without compromising the covertness of the measurement when using an n-mode state or making n uses of the channel.

## Quantum biology paper published in J. Phys. Chem. Lett.

George, Luke, and Animesh have recently had a paper published in The Journal of Physical Chemistry Letters (DOI: 10.1021/acs.jpclett.7b00829) in collaboration with Patrick Rowe and Alessandro Troisi (both formerly Warwick Chemistry, now UCL and Liverpool respectively). In this latest work they explore the relationship between structure and energy transport on the nanoscale. In particular, they look at 50,000 different ways of arranging 6 bacteriochlorophyll molecules between a fixed input and output molecule. One such arrangement is the naturally occurring one found in the famous Fenna-Matthews-Olsen (FMO) light-harvesting complex — a prototypical component of photosynthesis. Whether the FMO has been adapted to support very efficient transport of a quantum of energy from where it is absorbed (elsewhere in the organism, eventually arriving at the 'input') to the reaction centre (the ‘output’, where it is stored as chemical energy) is a long-standing question. By looking at many alternative structures, one can gain some insight into this puzzle, and also try to identify which structural features of a general structure are important for optimising energy transport. Such insight would likely be very useful in designing artificial energy transport structures such as those found in solar cells.

## George published in NJP

With his latest publication in the New Journal of Physics (DOI: 10.1088/1367-2630/aa54ab), George has proposed experimental tests which can further constrain the extent to which the wavefunction can be epistemic (and thus representing only a lack of knowledge as to the true physical state of reality).

## Quantum metrology paper in PRA

Christos, Dominic and Animesh's paper on quantum-enhanced estimation of multiple phase parameters has been published in Physical Review A. It looks at fundamental bounds on the performance of Gaussian states for estimation of multiple phase parameters and the advantage gained over multiple individual estimation strategies. The results also suggest that the optimal states for single phase estimation do not necessarily have the same performance when generalised to the estimation of multiple similar parameters.