Minimum time for the evolution to an orthogonal quantum state

Pulak Ranjan Giri

Haidong Yuan, Chi‐Hang Fred Fung

The laws of quantum physics place a limit on the speed of computation, in particular the evolution time of a system cannot be arbitrarily fast. Bounds on the speed of evolution for unitary dynamics have been long studied. A few bounds on the speed of evolution for noisy dynamics have also been obtained recently, these bounds, however, are in general not tight. In this article we present a new framework for quantum speed limit of noisy dynamics. With this framework we obtain the exact maximal angle that a noisy dynamics can achieve at any given time, this then provides tight bounds on the evolution time for noisy dynamics. The obtained bound reveals that noisy dynamics are generically different from unitary dynamics, in particular we show that the 'orthogonalization' time, which is the minimum time needed to evolve any state to its orthogonal states, is in general not applicable to noisy dynamics.

Kazutaka G. Nakamura

Soroush Haseli, S. Salimi

Abstract The minimum time a system needs to change from an initial state to a final orthogonal state is called the quantum speed limit time. The quantum speed limit time can be used to quantify the speed of the quantum evolution. The speed of the quantum evolution will increase, if the quantum speed limit time decreases. In this work, we will use a relative purity-based bound for the quantum speed limit time. This work is applicable for any arbitrary initial state. Here, we investigate the effects of a filtering operation on the quantum speed limit time. It will be observed that for some intervals of the filtering operation parameter, the quantum speed limit time is decreased by increasing the filtering operation parameter and for some other intervals it is decreased by decreasing the filtering operation parameter.

YOSUKE OKUDAIRA

Simon Rochester, M. P. Ledbetter, T. Zigdon +2 more

The relationship between orientation-to-alignment conversion (a form of atomic polarization evolution induced by an electric field) and the phenomenon of spin squeezing is demonstrated. A ``stretched'' state of an atom or molecule with maximum angular-momentum projection along the quantization axis possesses orientation and is a quantum-mechanical minimum-uncertainty state, where the product of the equal uncertainties of the angular-momentum projections on two orthogonal directions transverse to the quantization axis is the minimum allowed by the uncertainty relation. Application of an electric field for a short time induces orientation-to-alignment conversion and produces a spin-squeezed state, in which the quantum state essentially remains a minimum-uncertainty state, but the uncertainties of the angular-momentum projections on the orthogonal directions are unequal. This property can be visualized using the angular-momentum probability surfaces, where the radius of the surface is given by the probability of measuring the maximum angular-momentum projection in that direction. Brief remarks are also given concerning collective-spin squeezing and quantum nondemolition measurements.