Measurement- and comparison-based sizes of Schrödinger cat states of light

We extend several measurement-based definitions of effective superposition size to coherent state superpositions with branches composed of either single coherent states or tensor products of coherent states. These measures of superposition size depend on determining the maximal quantum distinguishability of certain states associated with the superposition state: e.g., in one measure, the maximal distinguishability of the branches of the superposition is considered as in quantum binary decision theory; in another measure, the maximal distinguishability of the initial superposition and its image after a one-parameter evolution generated by a local Hermitian operator is of interest. The scaling of the size of the superposition with the number of modes and mode intensity (i.e., photon number) is compared to the scaling of certain geometric properties of the Wigner function of the superposition and also to the superposition size estimated experimentally from decoherence. We also apply earlier comparison-based methods for determining macroscopic superposition size that require a reference Greenberger-Horne-Zeilinger (GHZ) state. The case of a hierarchical Schrödinger cat state with branches composed of smaller superpositions is also analyzed from a measurement-based perspective. © 2014 American Physical Society

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

Electrooptical scanning of film

Scan-in scan-out flying spot scanning system recognizes three different levels of transmissivity within a frame. It selectively acts on these levels either to intensify the illumination or to extend the duration of the illuminating spot to any picture element. Thus it improves the ratio of signal to tube noise in the cameras output

Amplification of the quantum superposition macroscopicity of a flux qubit by a magnetized Bose gas

We calculate a measure of superposition macroscopicity $\mathcal{M}$ for a superposition of screening current states in a superconducting flux qubit (SFQ), by relating $\mathcal{M}$ to the action of an instanton trajectory connecting the potential wells of the flux qubit. When a magnetized Bose-Einstein condensed (BEC) gas containing $N_{B}\sim \mathcal{O}(10^6)$ atoms is brought into a $\mathcal{O}(1)$ $\mu\text{m}$ proximity of the flux qubit in an experimentally realistic geometry, we demonstrate the appearance of a two- to five-fold amplification of $\mathcal{M}$ over the bare value without the BEC, by calculating the instantion trajectory action from the microscopically derived effective flux Lagrangian of a hybrid quantum system composed of the flux qubit and a spin-$F$ atomic Bose gas. Exploiting the connection between $\mathcal M$ and the maximal metrological usefulness of a multimode superposition state, we show that amplification of $\mathcal{M}$ in the ground state of the hybrid system is equivalent to a decrease in the quantum Cram\'{e}r-Rao bound for estimation of an externally applied flux. Our result therefore demonstrates the increased usefulness of the BEC--SFQ hybrid system as a sensor of ultraweak magnetic fields below the standard quantum limit.Comment: 10 pages, 2 figure