Optimal Entropy Compression in Quantum Bits

Global unitary transformations (optswaps) that optimally increase the bias of any mixed computation qubit in a quantum system – represented by a diagonal density matrix – towards a particular state of the computational basis which, in effect, increases its purity are presented. Quantum circuits that achieve this by implementing the above data compression technique – a generalization of the 3B-Comp [Fernandez, Lloyd, Mor, Roychowdhury (2004); arXiv:quant-ph/0401135] used before – are described. These circuits enable purity increment in the computation qubit by maximally transferring part of its von Neumann or Shannon entropy to any number of surrounding qubits starting with arbitrary initial biases. Using the optswaps, a practicable new method that algorithmically achieves hierarchy-dependent cooling of qubits to their respective limits in an engineered quantum register opened to the environment is delineated. In addition to fundamental quantum thermodynamic interests, this work may be important towards satisfying the DiVincenzo criterion for qubit initialization in some quantum computing architectures.