Stability of quantum states of finite macroscopic systems against classical noises, perturbations from environments, and local measurements

Abstract

We study the stability of quantum states of macroscopic systems of finite volume V, against weak classical noises (WCNs), weak perturbations from environments (WPEs), and local measurements (LMs). We say that a pure state is `fragile' if its decoherence rate is anomalously great, and `stable against LMs' if the result of a LM is not affected by another LM at a distant point. By making full use of the locality and huge degrees of freedom, we show the following: (i) If square fluctuation of every additive operator is O(V) or less for a pure state, then it is not fragile in any WCNs or WPEs. (ii) If square fluctuations of some additive operators are O(V^2) for a pure state, then it is fragile in some WCNs or WPEs. (iii) If a state (pure or mixed) has the `cluster property,' then it is stable against LMs, and vice versa. These results have many applications, among which we discuss the mechanism of symmetry breaking in finite systems.

6 pages, no figure.Proof of the theorem is described in the revised manuscript

References in corpus (1)

• Energies and collapse times of symmetric and symmetry-breaking states of finite systems with a U(1) symmetry

Cited by in corpus (63)

• Canonical Thermal Pure Quantum State
• Macroscopic quantum states: measures, fragility and implementations
• Quantum Zeno effect by general measurements
• Not all pure entangled states are useful for sub shot-noise interferometry
• Measures of macroscopicity for quantum spin systems
• Thermofield dynamics: Quantum Chaos versus Decoherence
• Detection of Macroscopic Entanglement by Correlation of Local Observables
• Ensemble based quantum metrology
• Macroscopic entanglement of many-magnon states
• Linking Measures for Macroscopic Quantum States via Photon-Spin Mapping
• Investigating macroscopic quantum superpositions and the quantum-to-classical transition by optical parametric amplification
• Characterizations and Quantifications of Macroscopic Quantumness and Its Implementations using Optical Fields
• Shortcuts to adiabatic cat-state generation in bosonic Josephson junctions
• All macroscopic quantum states are fragile and hard to prepare
• Stability of encoded macroscopic quantum superpositions
• Two-mode squeezed states as Schrodinger-cat-like states
• Strong entanglement causes low gate fidelity in inaccurate one-way quantum computation
• Classification of macroscopic quantum effects
• Quantum metrology with generalized cat states
• Superposition of macroscopically distinct states means large multipartite entanglement
• Fragility of quantum correlations and coherence in a multipartite photonic system
• Spontaneous symmetry breaking induced by quantum monitoring
• Quantum macroscopicity versus distillation of macroscopic superpositions
• Disturbance-Based Measure of Macroscopic Coherence
• Are cloned quantum states macroscopic?
• Is macroscopic entanglement a typical trait of many-particle quantum states?
• Quantum Violation of Fluctuation-Dissipation Theorem
• Quantum macroscopicity measure for arbitrary spin systems and its application to quantum phase transitions
• Detecting the degree of macroscopic quantumness using an overlap measurement
• Correlations of observables in chaotic states of macroscopic quantum systems
• Appearance and Stability of Anomalously Fluctuating States in Shor's Factoring Algorithm
• Scaling of macroscopic superpositions close to a quantum phase transition
• Fast generation of Cat states in Kerr nonlinear resonators via optimal adiabatic control
• Decoherence rate in random Lindblad dynamics
• Macroscopic superpositions as quantum ground states
• Visualization of superposition of macroscopically distinct states
• Lower bounds on the size of general Schrödinger-cat states from experimental data
• Quantum spin systems versus Schroedinger operators: A case study in spontaneous symmetry breaking
• Conversion of Thermal Equilibrium States into Superpositions of Macroscopically Distinct States
• Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking
• Low-temperature coherence properties of Z_2 quantum memory
• On the limitations of a measurement-assisted optomechanical route to quantum macroscopicity of superposition states
• On the size of linear superpositions in molecular nanomagnets
• Stability of Quantum Statistical Ensembles with Respect to Local Measurements
• Universal Property of Quantum Measurements of Equilibrium Fluctuations and Violation of Fluctuation-Dissipation Theorem
• Emergence of a thermal equilibrium in a subsystem of a pure ground state by quantum entanglement
• Growing Schrödinger's cat states by local unitary time evolution of product states
• Macroscopic Schrödinger Cat Resistant to Particle Loss and Local Decoherence
• Detecting Macroscopic Indefiniteness of Cat States in Bosonic Interferometers
• Stability and Absence of a Tower of States in Ferrimagnets
• Correlations in local measurements and entanglement in many-body systems
• Local Decoherence-free Macroscopic Quantum states
• Amplification of the quantum superposition macroscopicity of a flux qubit by a magnetized Bose gas
• Sequentially generated entanglement, macroscopicity and squeezing in a spin chain
• Superposition of Macroscopically Distinct States in Adiabatic Quantum Computation
• Tree-size complexity of multiqubit states
• Macroscopic Schrödinger-cat states of nonequilibrium electrons induced by cat-state optical driving and projective measurements on the light field
• Macroscopic quantumness of optically conditioned mechanical systems
• Decoherence of nonrelativistic bosonic quantum fields
• Pancharatnam phase deficit can detect macroscopic entanglement
• Quantifying Stability of Quantum Statistical Ensembles
• Protected Rabi oscillation induced by natural interactions among physical qubits
• Coherence Based Characterization of Macroscopic Quantumness