Stability of Macroscopic Quantum States against Perturbations from Environments and Local Measurement

Akira Shimizu, Takayuki Miyadera

We study the stability of quantum states of macroscopic systems of finite volume V. By using both 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 for any weak classical noises or weak perturbations from environments. (ii) If square fluctuation of some additive operator is O(V2) for a pure state, then it is fragile for some of these. (iii) If a state, pure or mixed, has the "cluster property," then it is stable against local measurements, and vice versa. Among many applications, we discuss the mechanism of symmetry-breaking in finite systems.

Andrea López-Incera

Philip R. Wallace

Akira Shimizu, Takayuki Miyadera, Akihisa Ukena

We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which describes the strength of spatial correlations of fluctuations of local observables, and to fluctuations of additive operators. The present theory has many applications, among which we discuss the mechanism of phase transitions in finite systems and quantum computers with a huge number of qubits.

Luis Roa, A. Krügel, C. Saavedra

Roland L. Omnes

A brief review is given of the present state of an approach to consistency between basic quantum mechanics and a unique macroscopic reality, with no assumption of branching in the state of the universe. The main new idea consists in the recognition of local properties in the growth and transport of entanglement between a macroscopic measuring quantum system and a microscopic measured one. Moving waves of entanglement from the environment arise then and carry external phases, affecting significantly the state of the measuring device. These "predecoherence" waves perturb randomly the growth of other waves, which carry entanglement with the measured system. The outcome of these wave interactions could generate random fluctuations in the quantum probabilities of different measurement channels, which could lead in turn to a collapse mechanism satisfying Born's probability rule, according to earlier works by Nelson and Pearle. A necessary randomness in the environment remains however unexplained and some suggestions regarding algorithmic complexity of the wave functions in a large quantum system e are made along that direction.