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

Abstract

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.

References in corpus (28)

• Advances in Quantum Metrology
• Quantum-enhanced measurements: beating the standard quantum limit
• Quantum metrology
• The maximum speed of dynamical evolution
• Entanglement, Non-linear Dynamics, and the Heisenberg Limit
• Generalized uncertainty relations: Theory, examples, and Lorentz invariance
• On the role of entanglement in quantum computational speed-up
• Dynamically protected cat-qubits: a new paradigm for universal quantum computation
• Environment-independent decoherence rate in classically chaotic systems
• Testing the limits of quantum mechanical superpositions
• Topological Order and Conformal Quantum Critical Points
• Interaction-based quantum metrology showing scaling beyond the Heisenberg limit
• Macroscopicity of Mechanical Quantum Superposition States
• Schrodinger cats and their power for quantum information processing
• Weak force detection with superposed coherent states
• Measures of macroscopicity for quantum spin systems
• Quantification of Macroscopic Quantum Superpositions within Phase Space
• Quantum-limited metrology with product states
• On the effective size of certain "Schrödinger cat'' like states
• A measurement-based measure of the size of macroscopic quantum superpositions
• Kind of entanglement that speeds up quantum evolution
• Measuring the size of a Schroedinger cat state
• Ultimate limits to quantum metrology and the meaning of the Heisenberg limit
• A size criterion for macroscopic superposition states
• Quantum speed limits and optimal Hamiltonians for driven systems in mixed states
• Two-Photon Algebra Eigenstates: A Unified Approach to Squeezing
• Measurement- and comparison-based sizes of Schrödinger cat states of light
• Electronic structure of superposition states in flux qubits

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• Macroscopic quantum states: measures, fragility and implementations
• "Photonic" cat states from strongly interacting matter waves
• Is macroscopic entanglement a typical trait of many-particle quantum states?
• Nonclassical properties and quantum resources of hierarchical photonic superposition states
• Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball
• Amplification of the quantum superposition macroscopicity of a flux qubit by a magnetized Bose gas