From stabilizer states to stabilizer channels

The stabilizer formalism was originally introduced to describe quantum error-correcting codes, but now plays many different roles in quantum information and quantum computation. The key idea of this formalism is that quantum states can be represented by operators that stabilize them. A quantum system is fully described by a quantum state, which is viewed as a mathematical object. The description of quantum states is a complicated task, because we need exponentially many parameters in the number of qubits. The stabilizer formalism is a powerful tool to describe a considerable class of entangled states. In this talk, we discuss various aspects of this formalism in the measurement process, entanglement detection, error correction, communication and computation. This talk is based on the following article: https://m.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=front&paperid=1&option_lang=rus