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Quadrature Coherence Scale Driven Fast Decoherence of Bosonic States

Both in order to obtain an ever better understanding of quantum physics and to solve problems in quantum information theory, there is continued interest in the exploration of the classical-quantum boundary and the identification of those quantum states exhibiting specifically quantum features, such as coherence and interference that cannot be explained with classical mechanics and/or classical probability theory.
We introduce, for each state of a bosonic quantum field, its quadrature coherence scale (QCS), a measure of the range of its quadrature coherences. Under coupling to a thermal bath, the purity and QCS are shown to decrease on a timescale inversely proportional to the QCS squared. The states most fragile to decoherence are therefore those with quadrature coherences far from the diagonal. We further show a large QCS is difficult to measure since it induces small scale variations in the state’s Wigner function. These two observations imply a large QCS constitutes a mark of “macroscopic coherence.” Finally, we link the QCS to optical classicality: optical classical states have a small QCS and a large QCS implies strong optical nonclassicality.