Yoon-Ho Kim: Non-physical operations for quantum information

Abstract

In quantum information processing, pure state qubits are prepared, quantum gates transform the initial state of the qubits, and the resulting state is stored in quantum memory for further processing or is measured. The quantum gate must operate so that the initial qubit state is unitarily transformed and this is due to the fundamental principle of quantum theory that positive operators are interpreted as probabilities via the Born rule. In other words, an anti-unitary transformation is not allowed in quantum theory. There exit, however, certain non-physical (i.e., mathematical) operations, which have important applications in quantum information and one such example is the transpose operation. The transpose operation has an important application in quantum information as the partial transpose operation on a two-qubit system can be used to detect entanglement in a universal way, i.e., no a priori information about the quantum state is needed.

In this talk, I will discuss how to optimally implement the universal transpose operation on a single-qubit system and the partial transpose operation on a two-qubit system using the method known as the structural physical approximation to positive maps. The experimental implementation is based on single-photon polarization qubits, linear optics, LOCC (local operation and classical communication).