Entanglement assisted metrology

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.

Thermodynamic precision in the nonequilibrium exchange scenario

We discuss exchange scenario thermodynamic uncertainty relations for the work done on a two-qubit entangled nonequilibrium steady state obtained by coupling the two qubits and putting each of them in weak contact with a thermal bath. In this way we investigate the use of entangled nonequilibrium steady states as end points of thermodynamic cycles. In this framework we prove analytically that for a paradigmatic unitary it is possible to construct an exchange scenario thermodynamic uncertainty relation. However, despite holding in many cases, we also show that such a relation ceases to be valid when considering other suitable unitary quenches. Furthermore, this paradigmatic example allows us to shed light on the role of the entanglement between the two qubits for precise work absorption. By considering the projection of the entangled steady state onto the set of separable states, we provide examples where such projection implies an increase of the relative uncertainty, showing the usefulness of entanglement.

Star-topology registers: NMR and quantum information perspectives

Quantum control of large spin registers is crucial for many applications ranging from spectroscopy to quantum information. A key factor that determines the efficiency of a register for implementing a given information processing task is its network topology. One particular type, called star-topology, involves a central qubit uniformly interacting with a set of ancillary qubits. A particular advantage of the star-topology quantum registers is in the efficient preparation of large entangled states, called NOON states, and their generalized variants. Thanks to the robust generation of such correlated states, spectral simplicity, ease of polarization transfer from ancillary qubits to the central qubit, as well as the availability of large spin-clusters, the star-topology registers have been utilized for several interesting applications over the last few years. Here we review some recent progress with the star-topology registers, particularly via nuclear magnetic resonance methods.

Quantum metrology in open systems: dissipative Cramér-Rao bound

Estimation of parameters is a pivotal task throughout science and technology. The quantum Cramér-Rao bound provides a fundamental limit of precision allowed to be achieved under quantum theory. For closed quantum systems, it has been shown how the estimation precision depends on the underlying dynamics. Here, we propose a general formulation for metrology scenarios in open quantum systems, aiming to relate the precision more directly to properties of the underlying dynamics. This feature may be employed to enhance an estimation precision, e.g., by quantum control techniques. Specifically, we derive a Cramér-Rao bound for a fairly large class of open system dynamics, which is governed by a (time-dependent) dynamical semigroup map. We illustrate the utility of this scenario through three examples.

Scalable spin amplification with a gain over a hundred

We propose a scalable and practical implementation of spin amplification which does not require individual addressing nor a specially tailored spin network. We have demonstrated a gain of 140 in a solid-state nuclear spin system of which the spin polarization has been increased to 0.12 using dynamic nuclear polarization with photoexcited triplet electron spins. Spin amplification scalable to a higher gain opens the door to the single spin measurement for a readout of quantum computers as well as practical applications of nuclear magnetic resonance spectroscopy to infinitesimal samples which have been concealed by thermal noise.

Environment-assisted precision measurement

We describe a method to enhance the sensitivity of precision measurements that takes advantage of the environment of a quantum sensor to amplify the response of the sensor to weak external perturbations. An individual qubit is used to sense the dynamics of surrounding ancillary qubits, which are in turn affected by the external field to be measured. The resulting sensitivity enhancement is determined by the number of ancillas that are coupled strongly to the sensor qubit; it does not depend on the exact values of the coupling strengths and is resilient to many forms of decoherence. The method achieves nearly Heisenberg-limited precision measurement, using a novel class of entangled states. We discuss specific applications to improve clock sensitivity using trapped ions and magnetic sensing based on electronic spins in diamond.

Bootstrap tomography of the pulses for quantum control

Long-time dynamical decoupling and quantum control of qubits require high-precision control pulses. Full characterization (quantum tomography) of imperfect pulses presents a bootstrap problem: tomography requires initial states of a qubit which cannot be prepared without perfect pulses. We present a protocol for pulse error analysis, specifically tailored for a wide range of the single solid-state electron spins. Using a single electron spin of a nitrogen-vacancy center in diamond, we experimentally verify the correctness of the protocol, and demonstrate its usefulness for quantum control tasks.

Strong correlations in quantum vortex nucleation of ultracold atomic gases

We review some recent developments in the theory of rotating atomic gases. These studies have thrown light on the process of nucleation of vortices in regimes where mean-field methods are inadequate. In our review, we shall describe and compare quantum vortex nucleation of a dilute ultracold bosonic gas trapped in three different configurations: a one-dimensional ring lattice, a one-dimensional ring superlattice and a two-dimensional asymmetric harmonic trap. In all of them, there is a critical rotation frequency, at which the particles in the ground state exhibit strong quantum correlations. However, the entanglement properties vary significantly from case to case. We explain these differences by characterizing the intermediate states that participate in the vortex nucleation process. Finally, we show that noise correlations are sensitive to these differences. These new studies have, therefore, shown how novel quantum states may be produced and probed in future experiments with rotating neutral atom systems.

NMR method for amplification of single-spin state

Amplification of a single-spin state using nuclear magnetic resonance (NMR) techniques in a rotating frame is considered. The main aim is to investigate the efficiency of various schemes for quantum detection. Results of numerical simulation of the time dependence of individual and total nuclear polarizations for 1D, 2D, and 3D configurations of the spin systems are presented.

Unifying quantum state transfer and state amplification

We present a Hamiltonian that can be used for amplifying the signal from a quantum state, enabling the measurement of a macroscopic observable to determine the state of a single spin. We prove a general mapping between this Hamiltonian and an exchange Hamiltonian for arbitrary coupling strengths and local magnetic fields. This facilitates the use of existing schemes for perfect state transfer to give perfect amplification. We further prove a link between the evolution of this fixed Hamiltonian and classical cellular automata, thereby unifying previous approaches to this amplification task. Finally, we show how to use the new Hamiltonian for perfect state transfer in the scenario where total spin is not conserved during the evolution, and demonstrate that this yields a significantly different response in the presence of decoherence.

Single spin measurement using cellular automata techniques

We analyze a conceptual approach to single-spin measurement. The method uses techniques from the theory of quantum cellular automata to correlate a large number of ancillary spins to the one to be measured. It has the distinct advantage of being efficient: under ideal conditions, it requires the application of only O((3)square root N)) steps (each requiring a constant number of rf pulses) to create a system of N correlated spins. Numerical simulations suggest that it is also, to a certain extent, robust against pulse errors, and imperfect initial polarization of the ancilla spin system.

Multiple-quantum NMR spin dynamics of inhomogeneous one-dimensional systems in solids

Multiple-quantum NMR spin dynamics of inhomogeneous one-dimensional systems in solids is investigated by analytical and numerical methods. A fermion approach for MQ spin dynamics of one-dimensional inhomogeneous systems is developed in the approximation of the dipole-dipole interactions (DDI) of nearest neighbors. It is shown that only MQ coherences of the zeroth and plus/minus second orders appear in the approximation of the DDI of the nearest neighbors even in inhomogeneous one-dimensional systems. We also investigate MQ dynamics of inhomogeneous chains numerically. Intensities of MQ NMR coherences for a linear chain consisting of 3000 spins are calculated.

Entanglement generation of nearly random operators

We study the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way. These include interpolating ensemble matrices, where the interval of the independent random parameters are restricted, pseudorandom operators, where there are far fewer random parameters than required for random matrices, and quantum chaotic evolution. Restricting randomness in different ways allows us to probe connections between entanglement and randomness. We comment on which properties affect entanglement generation and discuss ways of efficiently producing random states on a quantum computer.

Experimental demonstration of quantum state expansion in a cluster of dipolar-coupled nuclear spins

It is experimentally demonstrated that an arbitrary quantum state of a single spin 1/2, a| upward arrow+b| downward arrow, can be converted into a superposition of the two ferromagnetic states of a spin cluster: a| upward arrow upward arrow... upward arrow upward arrow+b| downward arrow downward arrow... downward arrow downward arrow. The physical system is a cluster of seven dipolar-coupled nuclear spins of single-labeled 13C-benzene molecules in a liquid-crystalline matrix. In this complex system, the pseudopure ground state and the required controlled unitary transformations have been implemented. The experimental scheme can be considered as an explicit model of quantum measurement.