Er'el Granot

Additional information is available at the end of the chapter Er'el Granot Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70395

#### Abstract

The way data is lost from the wavefunction in quantum dynamics is analyzed. The main results are (A) Quantum dynamics is a dispersive process in which any data initially encoded in the wavefunction is gradually lost. The ratio between the distortion's variance and the mean probability density increases in a simple form. (B) For any given amount of information encoded in the wavefunction, there is a time period, beyond which it is impossible to decode the data. (C) The temporal decline of the maximum information density in the wavefunction has an exact analytical expression. (D) For any given time period there is a specific detector resolution, with which the maximum information can be decoded. (E) For this optimal detector size the amount of information is inversely proportional to the square root of the time elapsed.

DOI: 10.5772/intechopen.70395

Keywords: quantum information, quantum encryption, uncertainty principle, quantum decoding

## 1. Introduction

The field of quantum information received a lot of attention recently due to major development in quantum computing [1–5], quantum cryptography, and quantum communications [6–8].

In most quantum computing, the wavefunction is a superposition of multiple binary states (qubits), which can be in spin states, polarization state, binary energy levels, etc. However, since the wavefucntion is a continuous function, it can carry, in principle, an infinite amount of information. Only the detector dimensions and noises limits the information capacity.

The quantum wavefunction, like any complex signal, carries a large amount of information, which can be decoded in the detection process. Its local amplitude can be detected by measuring the probability density in a direct measurement, while its phase can be retrieved in an interferometric detection, just as in optical coherent detection [9].

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The amount of information depends on the detector's capabilities, i.e., it depends on the detector's spatial resolution and its inner noise level. Therefore, the maximum amount of information that can be decoded from the wavefunction is determined by the detector's characteristics. However, unlike the classical wave equation, the quantum Schrödinger dynamics is a dispersive process. During the quantum dynamics, the wavefunction experiences distortions. These distortions increase in time just like the dispersion effects on signals in optical communications [10, 11].

Nevertheless, unlike dispersion compensating modules in optical communications, there is no way to compensate or "undo" the dispersive process in quantum mechanics. Therefore, the amount of information that can be decoded decreases monotonically with time.

The object of this chapter is to investigate the way information is lost during the quantum dynamics.
