English

Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with Applications

Quantum Physics 2014-11-18 v2 General Relativity and Quantum Cosmology High Energy Physics - Theory

Abstract

We derive differential equations for the modified Feynman propagator and for the density operator describing time-dependent measurements or histories continuous in time. We obtain an exact series solution and discuss its applications. Suppose the system is initially in a state with density operator ρ(0)\rho(0) and the projection operator E(t)=U(t)EU(t)E(t) = U(t) E U^\dagger(t) is measured continuously from t=0t = 0 to TT, where EE is a projector obeying Eρ(0)E=ρ(0)E\rho(0) E = \rho(0) and U(t)U(t) a unitary operator obeying U(0)=1U(0) = 1 and some smoothness conditions in tt. Then the probability of always finding E(t)=1E(t) = 1 from t=0t = 0 to TT is unity. Generically E(T)EE(T) \neq E and the watched system is sure to change its state, which is the anti-Zeno paradox noted by us recently. Our results valid for projectors of arbitrary rank generalize those obtained by Anandan and Aharonov for projectors of unit rank.

Keywords

Cite

@article{arxiv.quant-ph/0102019,
  title  = {Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with Applications},
  author = {A. P. Balachandran and S. M. Roy},
  journal= {arXiv preprint arXiv:quant-ph/0102019},
  year   = {2014}
}

Comments

16 pages, latex; new material and references added

R2 v1 2026-07-22T19:30:08.270Z