Recent examples have confirmed the common belief that quantum chaos is always suppressed in the presence of an environment. Here we show that this is not always the case. We compute the Lyapunov exponent of a
q-body Majorana Sachdev-Ye-Kitaev (SYK) model coupled to a Markovian bath. Provided that the jump operators describing the bath are isotropic random
k>2-body Majoranas fields, the Lyapunov exponent is positive for any strength of the coupling to the bath. Interestingly, this also applies to
q=2 where the SYK is integrable which indicates that many-body quantum chaos can be induced by the environment. Moreover, for
q>2, where the unitary dynamics is quantum chaotic, and sufficiently large
k, the Lyapunov exponent increases with the coupling to the bath. Explicit analytical results are obtained in the
q=2 and large
q limits. Our results put forward an alternate route to induce and control the generation of scrambling in quantum many-body systems which is of potential relevance in the design of quantum information devices.
Chaos in classical systems can be characterized by Lyapunov exponents that measure the exponential divergence of nearby trajectories, but directly extending this framework to quantum mechanics has been a persistent challenge. The wavelike nature of quantum states and the non-commutative geometry of quantum phase space obstruct a straightforward generalization of classical chaos theory. Here we develop a rigorous approach to quantum chaos by leveraging quantum optimal transport theory, which provides the missing geometric foundation for measuring distances between extended quantum distributions. We define quantum Lyapunov exponents that naturally avoid divergences encountered when naïvely generalizing classical exponents, and show that in the semiclassical limit they recover the classical global expansion rate, and hence the usual maximal Lyapunov exponent when they coincide. Our framework provides a tight connection between the divergence of classical trajectories and semiclassical phase space evolution, and additionally clarifies the role of out-of-time-order correlators as diagnostics of quantum chaos. These results establish quantum optimal transport as a unifying mathematical foundation for quantum chaos theory, providing new tools to characterize dynamical behavior across the full range of quantum dynamics from simple few-body models to complex many-body systems.