Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space

We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary distinguishability of the branches of the superposition and another based on the ratio of the maximal quantum Fisher information of the superposition to that of its branches, i.e., the relative metrological usefulness of the superposition. A general formula for the effective sizes of these states according to the branch distinguishability measure is obtained and applied to superposition states of $N$ quantum harmonic oscillators composed of Gaussian branches. Considering optimal distinguishability of pure states on a time-evolution path leads naturally to a notion of distinguishability time that generalizes the well known orthogonalization times of Mandelstam and Tamm and Margolus and Levitin. We further show that the distinguishability time provides a compact operational expression for the superposition size measure based on the relative quantum Fisher information. By restricting the maximization procedure in the definition of this measure to an appropriate algebra of observables, we show that the superposition size of, e.g., N00N states and hierarchical cat states, can scale linearly with the number of elementary particles comprising the superposition state, implying precision scaling inversely with the total number of photons when these states are employed as probes in quantum parameter estimation of a 1-local Hamiltonian in this algebra

Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball

For both unitary and open qubit dynamics, we compare asymmetry monotone-based bounds on the minimal time required for an initial qubit state to evolve to a final qubit state from which it is probabilistically distinguishable with fixed minimal error probability (i.e., the minimal error distinguishability time). For the case of unitary dynamics generated by a time-independent Hamiltonian, we derive a necessary and sufficient condition on two asymmetry monotones that guarantees that an arbitrary state of a two-level quantum system or a separable state of $N$ two-level quantum systems will unitarily evolve to another state from which it can be distinguished with a fixed minimal error probability $\delta \in [0,1/2]$. This condition is used to order the set of qubit states based on their distinguishability time, and to derive an optimal release time for driven two-level systems such as those that occur, e.g., in the Landau-Zener problem. For the case of non-unitary dynamics, we compare three lower bounds to the distinguishability time, including a new type of lower bound which is formulated in terms of the asymmetry of the uniformly time-twirled initial system-plus-environment state with respect to the generator $H_{SE}$ of the Stinespring isometry corresponding to the dynamics, specifically, in terms of $\Vert [H_{SE},\rho_{\text{av}}(\tau)]\Vert_{1}$, where $\rho_{\text{av}}(\tau):={1\over \tau}\int_{0}^{\tau}dt\, e^{-iH_{SE}t}\rho \otimes \vert 0\rangle_{E}\langle 0\vert_{E} e^{iH_{SE}t}$.Comment: 13 pages, 4 figure

Continuous Measurement of a Non-Markovian Open Quantum System

Continuous quantum measurement is the backbone of various methods in quantum control, quantum metrology, and quantum information. Here, we present a generalized formulation of dispersive measurement of a complex quantum systems. We describe the complex system as an open quantum system that is strongly coupled to a non-Markovian environment, enabling the treatment of a broad variety of natural or engineered complex systems. The system is monitored via a probe resonator coupled to a broadband (Markovian) reservoir. Based on this model, we derive a formalism of Stochastic Hierarchy Equations of Motion (SHEM) describing the decoherence dynamics of the system conditioned on the measurement record. Furthermore, we demonstrate a spectroscopy method based on weak quantum measurement to reveal the non-Markovian nature of the environment, which we term weak spectroscopy.Comment: Published version, the section on continuous state tomography will be published in a separate manuscrip

OCS in small para-hydrogen clusters: energetics and structure with N=1-8 complexed hydrogen molecules

We determine the structure and energetics of complexes of the linear OCS molecule with small numbers of para-hydrogen molecules, N=1-8, using zero temperature quantum Monte Carlo methods. Ground state calculations are carried out with importance-sampled rigid body diffusion Monte Carlo (IS-RBDMC) and excited state calculations with the projection operator imaginary time spectral evolution (POITSE) methodology. The ground states are found to be highly structured, with a gradual build up of two axial rings as N increases to 8. Analysis of the azimuthal density correlations around the OCS molecule shows that these rings are quite delocalized for small N values, but become strongly localized for N \geq 5 . Excited state calculations are made for a range of total cluster angular momentum values and the rotational energy levels fitted to obtain effective rotational and distortion constants of the complexed OCS molecule as a function of cluster size N. Detailed analysis of these spectroscopic constants indicates that the complexes of OCS with para-hydrogen have an unusually rich variation in dynamical behavior, with sizes N=1-2 showing near rigid behavior, sizes N=3-4 showing extremely floppy behavior, and the larger sizes N=5-8 showing more rigid behavior again. The large values of the distortion constant D obtained for N=3-4 are rationalized in terms of the coupling between the OCS rotations and the "breathing" mode of the first, partially filled ring of para-hydrogen molecules.Comment: 26 pages, 11 figures. accepted for publication in the Journal of Chemical Physic

Stable quantum memories with limited measurement

We demonstrate the existence of a finite temperature threshold for a 1D stabilizer code under an error correcting protocol that requires only a fraction of the syndrome measurements. Below the threshold temperature, encoded states have exponentially long lifetimes, as demonstrated by numerical and analytical arguments. We sketch how this algorithm generalizes to higher dimensional stabilizer codes with string-like excitations, like the toric code.Comment: 11 Pages, 7 Figure