---
author:
- 'Sreetama Das$^{1,2}$, Titas Chanda$^{1,2}$, Maciej Lewenstein$^{3, 4}$, Anna Sanpera$^{4, 5}$, Aditi Sen(De)$^{1,2}$, and Ujjwal Sen$^{1,2}$'
title: |
    Lectures on Quantum Information\
    Chapter 1: The separability versus entanglement problem
---

Introduction
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Quantum theory, formalized in the first few decades of the 20$^{\mbox{th}}$century, contains elements that are radically different from the classical description of Nature. An important aspect in these fundamental differences is the existence of quantum correlations in the quantum formalism. In the classical description of Nature, if a system is formed by different subsystems, complete knowledge of the whole system implies that the sum of the information of the subsystems makes up the complete information for the whole system. This is no longer true in the quantum formalism. In the quantum world, there exist states of composite systems for which we might have the complete knowledge, while our knowledge about the subsystems might be completely random. In technical terms, one can have pure quantum states of a two-party system, whose local states are completely mixed. One may reach some paradoxical conclusions if one applies a classical description to states which have characteristic quantum signatures.

During the last two decades, it has been realized that these fundamentally 