Adaptive tracking of a time-varying field with a quantum sensor

Sensors based on single spins can enable magnetic field detection with very high sensitivity and spatial resolution. Previous work has concentrated on sensing of a constant magnetic field or a periodic signal. Here, we instead investigate the problem of estimating a field with non-periodic variation described by a Wiener process. We propose and study, by numerical simulations, an adaptive tracking protocol based on Bayesian estimation. The tracking protocol updates the probability distribution for the magnetic field, based on measurement outcomes, and adapts the choice of sensing time and phase in real time. By taking the statistical properties of the signal into account, our protocol strongly reduces the required measurement time. This leads to a reduction of the error in the estimation of a time-varying signal by up to a factor 4 compared to protocols that do not take this information into account.Comment: 10 pages, 6 figure

Loss-resistant unambiguous phase measurement

Entangled multi-photon states have the potential to provide improved measurement accuracy, but are sensitive to photon loss. It is possible to calculate ideal loss-resistant states that maximize the Fisher information, but it is unclear how these could be experimentally generated. Here we propose a set of states that can be obtained by processing the output from parametric down-conversion. Although these states are not optimal, they provide performance very close to that of optimal states for a range of parameters. Moreover, we show how to use sequences of such states in order to obtain an unambiguous phase measurement that beats the standard quantum limit. We consider the optimization of parameters in order to minimize the final phase variance, and find that the optimum parameters are different from those that maximize the Fisher information.Comment: 8 pages, 7 figures, comments are welcom

Relation between classical communication capacity and entanglement capability for two-qubit unitary operations

Two-qubit operations may be characterized by their capacities for communication, both with and without free entanglement, and their capacity for creating entanglement. We establish a set of inequalities that give an ordering to the capacities of two-qubit unitary operations. Specifically, we show that the capacities for entanglement creation and bidirectional communication without entanglement assistance are at least as great as half the bidirectional communication capacity with entanglement assistance. In addition, we show that the bidirectional communication that can be performed using an ensemble may be increased via a two-qubit unitary operation by twice the operation's capacity for entanglement.Comment: 12 pages, published version plus minor correction

Implementation of multipartite unitary operations with limited resources

A general method for implementing weakly entangling multipartite unitary operations using a small amount of entanglement and classical communication is presented. For the simple Hamiltonian \sigma_z\otimes\sigma_z this method requires less entanglement than previously known methods. In addition, compression of multiple operations is applied to reduce the average communication required.Comment: 7 pages, 4 figures, comments welcom

Black-box Hamiltonian simulation and unitary implementation

We present general methods for simulating black-box Hamiltonians using quantum walks. These techniques have two main applications: simulating sparse Hamiltonians and implementing black-box unitary operations. In particular, we give the best known simulation of sparse Hamiltonians with constant precision. Our method has complexity linear in both the sparseness D (the maximum number of nonzero elements in a column) and the evolution time t, whereas previous methods had complexity scaling as D^4 and were superlinear in t. We also consider the task of implementing an arbitrary unitary operation given a black-box description of its matrix elements. Whereas standard methods for performing an explicitly specified N x N unitary operation use O(N^2) elementary gates, we show that a black-box unitary can be performed with bounded error using O(N^{2/3} (log log N)^{4/3}) queries to its matrix elements. In fact, except for pathological cases, it appears that most unitaries can be performed with only O(sqrt{N}) queries, which is optimal.Comment: 19 pages, 3 figures, minor correction

Swarm optimization for adaptive phase measurements with low visibility

Adaptive feedback normally provides the greatest accuracy for optical phase measurements. New advances in nitrogen vacancy centre technology have enabled magnetometry via individual spin measurements, which are similar to optical phase measurements but with low visibility. The adaptive measurements that previously worked well with high-visibility optical interferometry break down and give poor results for nitrogen vacancy centre measurements. We use advanced search techniques based on swarm optimisation to design better adaptive measurements that can provide improved measurement accuracy with low-visibility interferometry, with applications in nitrogen vacancy centre magnetometry.Comment: 8 pages, 7 figures, comments welcom

Gate-efficient discrete simulations of continuous-time quantum query algorithms

We show how to efficiently simulate continuous-time quantum query algorithms that run in time T in a manner that preserves the query complexity (within a polylogarithmic factor) while also incurring a small overhead cost in the total number of gates between queries. By small overhead, we mean T within a factor that is polylogarithmic in terms of T and a cost measure that reflects the cost of computing the driving Hamiltonian. This permits any continuous-time quantum algorithm based on an efficiently computable driving Hamiltonian to be converted into a gate-efficient algorithm with similar running time.Comment: 28 pages, 2 figure

Efficiencies of Quantum Optical Detectors

We propose a definition for the efficiency that can be universally applied to all classes of quantum optical detectors. This definition is based on the maximum amount of optical loss that a physically plausible device can experience while still replicating the properties of a given detector. We prove that detector efficiency cannot be increased using linear optical processing. That is, given a set of detectors, as well as arbitrary linear optical elements and ancillary light sources, it is impossible to construct detection devices that would exhibit higher efficiencies than the initial set.Comment: 5 pages, 3 figure