Mixedness, Coherence and Entanglement in a Family of Three-Qubit States.

Joanna K Kalaga,Radosław Szczȩśniak,Wiesław Leoński,Jan Peřina

doi:10.3390/e24030324

Abstract

We consider a family of states describing three-qubit systems. We derived formulas showing the relations between linear entropy and measures of coherence such as degree of coherence, first- and second-order correlation functions. We show that qubit–qubit states are strongly entangled when linear entropy reaches some range of values. For such states, we derived the conditions determining boundary values of linear entropy parametrized by measures of coherence.

Highlights

Recent developments in modern physics showed that quantum correlations such as quantum entanglement and their relations to quantum coherence play a valid role in understanding the nature of various physical systems
For two-qubit states, we find possible values of linear entropy parametrized by both correlation functions considered here and derive the formulas which allow identifying ranges of values of discussed parameters for which strongly entangled states can be found
Applying the tracing out procedure, we have analyzed the degree of mixedness of such two-qubit states, the bipartite coherences, and entanglement

Summary

Introduction

Recent developments in modern physics showed that quantum correlations such as quantum entanglement and their relations to quantum coherence play a valid role in understanding the nature of various physical systems. The paper is organized as follows: in Section 2, we introduce two families of states describing the three-qubit systems of our interest We concentrate on the situation when we deal with a single excitation, so the total number of photons/phonons n = n1 + n2 + n3 = 1, where indices 1–3 label the qubits For such a case, the wave function describing the system’s state is. W-states can be employed, for instance, in quantum teleportation systems [65,66,67], dense coding [68,69,70], and cryptographic protocols [71,72]

The Linear Entropy and Degree of Coherence

The First-Order Correlation Function and Linear Entropy

The Second-Order Correlation Function and Linear Entropy

Conclusions

Results