This review introduces a new development in theoretical quantum physics, the ``resource-theoretic'' point of view. The approach aims to be closely linked to experiment, and to state exactly what result you can hope to achieve for what expenditure of effort in the laboratory. This development is an extension of the principles of thermodynamics to quantum problems; but there are resources that would never have been considered previously in thermodynamics, such as shared knowledge of a frame of reference. Many additional examples and new quantifications of resources are provided.

Quantum resource theories

We report the creation of thermal, Fock, coherent, and squeezed states of motion of a harmonically bound {sup 9}Be{sup +} ion. The last three states are coherently prepared from an ion which has been initially laser cooled to the zero point of motion. The ion is trapped in the regime where the coupling between its motional and internal states, due to applied (classical) radiation, can be described by a Jaynes-Cummings-type interaction. With this coupling, the evolution of the internal atomic state provides a signature of the number state distribution of the motion. {copyright} {ital 1996 The American Physical Society.}

Generation of Non-classical Motional States of a Trapped Atom

In the last two decades there has been an enormous progress in the experimental investigation of single quantum systems. This progress covers fields such as quantum optics, quantum computation, quantum cryptography, and quantum metrology, which are sometimes summarized as `quantum technologies'. A key issue there is entanglement, which can be considered as the characteristic feature of quantum theory. As disparate as these various fields maybe, they all have to deal with a quantum mechanical treatment of the measurement process and, in particular, the control process. Quantum control is, according to the authors, `control for which the design requires knowledge of quantum mechanics'. Quantum control situations in which measurements occur at important steps are called feedback (or feedforward) control of quantum systems and play a central role here. This book presents a comprehensive and accessible treatment of the theoretical tools that are needed to cope with these situations. It also provides the reader with the necessary background information about the experimental developments. The authors are both experts in this field to which they have made significant contributions. After an introduction to quantum measurement theory and a chapter on quantum parameter estimation, the central topic of open quantum systems is treated at some length. This chapter includes a derivation of master equations, the discussion of the Lindblad form, and decoherence – the irreversible emergence of classical properties through interaction with the environment. A separate chapter is devoted to the description of open systems by the method of quantum trajectories. Two chapters then deal with the central topic of quantum feedback control, while the last chapter gives a concise introduction to one of the central applications – quantum information. All sections contain a bunch of exercises which serve as a useful tool in learning the material. Especially helpful are also various separate boxes presenting important background material on topics such as the block representation or the feedback gain-bandwidth relation. The two appendices on quantum mechanics and phase-space and on stochastic differential equations serve the same purpose. As the authors emphasize, the book is aimed at physicists as well as control engineers who are already familiar with quantum mechanics. It takes an operational approach and presents all the material that is needed to follow research on quantum technologies. On the other hand, conceptual issues such as the relevance of the measurement process for the interpretation of quantum theory are neglected. Readers interested in them may wish to consult instead a textbook such as Decoherence and the Quantum-to-Classical Transition by Maximilian Schlosshauer. Although the present book does not contain applications to gravity, part of its content might become relevant for the physics of gravitational-wave detection and quantum gravity phenomenology. In this respect it should be of interest also for the readers of this journal.

https://iopscience.iop.org/article/10.1088/0264-9381/27/24/249002/pdf

Quantum Measurement and Control

Journal Of The American Statistical Association V-27

In the context of quantifying entanglement we study those functions of a multipartite state which do not increase under the set of local transformations. A mathematical characterization of these monotone magnitudes is presented. They are then related to optimal strategies of conversion of shared states. More detailed results are presented for pure states of bipartite systems. It is show that more than one measure are required simultaneously in order to quantify completely the non-local resources contained in a bipartite pure state, while examining how this fact does not hold in the so-called asymptotic limit. Finally, monotonicity under local transformations is proposed as the only natural requirement for measures of entanglement.

On the characterization of entanglement

We propose a set of protocols for verifying quantum computing at any time after the computation itself has been performed. We provide two constructions: one requires five entangled provers and a completely classical verifier; the other requires a single prover, a verifier, who is restricted to measuring qubits in the $X$ or $Z$ basis, and one-way quantum communication from the prover to the verifier. These results demonstrate that the verification can be achieved independently from the blindness. We also show that a constant round protocol with a single prover and a completely classical verifier is not possible, unless bounded error quantum polynomial time (BQP) is contained in the third level of the polynomial hierarchy.

Post hoc Verification of Quantum Computation.

It is desirable to observe synchronization of quantum systems in the quantum regime, defined by the low number of excitations and a highly nonclassical steady state of the self-sustained oscillator. Several existing proposals of observing synchronization in the quantum regime suffer from the fact that the noise statistics overwhelm synchronization in this regime. Here, we resolve this issue by driving a self-sustained oscillator with a squeezing Hamiltonian instead of a harmonic drive and analyze this system in the classical and quantum regime. We demonstrate that strong entrainment is possible for small values of squeezing, and in this regime, the states are nonclassical. Furthermore, we show that the quality of synchronization measured by the FWHM of the power spectrum is enhanced with squeezing.

/pdf/squeezing-enhances-quantum-synchronization-241z5y0bzk.pdf

Squeezing Enhances Quantum Synchronization.

As progress on experimental quantum processors continues to advance, the problem of verifying the correct operation of such devices is becoming a pressing concern. The recent discovery of protocols for verifying computation performed by entangled but non-communicating quantum processors holds the promise of certifying the correctness of arbitrary quantum computations in a fully device-independent manner. Unfortunately, all known schemes have prohibitive overhead, with resources scaling as extremely high degree polynomials in the number of gates constituting the computation. Here we present a novel approach based on a combination of verified blind quantum computation and Bell state self-testing. This approach has dramatically reduced overhead, with resources scaling as only O(m4lnm) in the number of gates.

Device-Independent Verifiable Blind Quantum Computation

In order to guarantee the output of a quantum computation, we usually assume that the component devices are trusted. However, when the total computation process is large, it is not easy to guarantee the whole system when we have scaling effects, unexpected noise, or unaccounted correlations between several subsystems. If we do not trust the measurement basis nor the prepared entangled state, we do need to be worried about such uncertainties. To this end, we proposes a "self-guaranteed" protocol for verification of quantum computation under the scheme of measurement-based quantum computation where no prior-trusted devices (measurement basis nor entangled state) are needed. The approach we present enables the implementation of verifiable quantum computation using the measurement-based model in the context of a particular instance of delegated quantum computation where the server prepares the initial computational resource and sends it to the client who drives the computation by single-qubit measurements. Applying self-testing procedures we are able to verify the initial resource as well as the operation of the quantum devices, and hence the computation itself. The overhead of our protocol scales as the size of the initial resource state to the power of 4 times the natural logarithm of the initial state's size.

Self-guaranteed measurement-based quantum computation

Several inequivalent definitions of the geometric measure of entanglement (GM) have been introduced and studied in the past. Here we review several known and new definitions, with the qualifying criterion being that for pure states the measure is a linear or logarithmic function of the maximal fidelity with product states. The entanglement axioms and properties of the measures are studied, and qualitative and quantitative comparisons are made between all definitions. Streltsov et al. [New J. Phys. 12, 123004 (2010)] proved the equivalence of two linear definitions of GM, whereas we show that the corresponding logarithmic definitions are distinct. Certain classes of states such as ``maximally correlated states'' and isotropic states are particularly valuable for this analysis. A little-known GM definition is found to be the first one to be both normalized and weakly monotonous, thus being a prime candidate for future studies of multipartite entanglement. We also find that a large class of graph states, which includes all cluster states, have a ``universal'' closest separable state that minimizes the quantum relative entropy, the Bures distance, and the trace distance.

Michal Hajdušek

Papers

Post hoc Verification of Quantum Computation.

Squeezing Enhances Quantum Synchronization.

Device-Independent Verifiable Blind Quantum Computation

Self-guaranteed measurement-based quantum computation

Comparison of different definitions of the geometric measure of entanglement