Steady state coherence and entanglement in a dissipative two-qubit system and its application for decision making

Abstract

Quantum decision theory was recently established based on the mathematics of Hilbert spaces to formalize the key concepts of quantum mechanics such as uncertainty and superposition that particularly manifest in cognitive processes. We aim to address how a two-qubit system interacting with a global squeezed vacuum field reservoir can be exploited as a black box model for quantum decision-making. To do so, we encode the input of the black box into the density matrix of the two-qubit system. The global reservoir drives the system towards its steady state via the decoherence process. The outcome of the black box can be obtained by performing measurement on the stationary state of the two-qubit system. We reveal that the squeezed reservoir can be used to control the coherence and entanglement of the black box’s output. Interestingly, it is shown that the steady state entanglement and coherence between two qubits, which have the same value, can be obtained by measuring the output state of the black box. Besides, we examine the potential application of the considered model for entanglement decision-making.