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While the microscopic laws of physics are often symmetric under time reversal, most natural processes that we observe are not. The emergent asymmetry between typical and time-reversed processes is referred to as the arrow of time. In quantum physics, an arrow of time emerges when a sequence of measurements is performed on a system. We introduce quantum control tools that can yield dynamics more consistent with time flowing backward than forward. The control tools are based on the explicit construction of a Hamiltonian that can replicate the stochastic trajectories of a monitored quantum system. Such a Hamiltonian can reverse the effect of monitoring and, via a feedback process, generate trajectories consistent with a reversed arrow of time. It can also be used to simulate the backward-in-time dynamics of an open quantum system. Finally, we design a feedback-driven continuous measurement engine powered by the energy pumped into the system by the monitoring process. We show that the engine can operate under experimentally realizable conditions with feedback delay and finite-efficiency measurements. 

We characterize the dynamical state of many-body bosonic and fermionic many-body models with intersite Gaussian couplings, on-site non-Gaussian interactions, and local dissipation comprising incoherent particle loss, particle gain, and dephasing. We first establish that, for fermionic systems, if the dephasing noise is larger than the non-Gaussian interactions, irrespective of the Gaussian coupling strength, the system state is a convex combination of Gaussian states at all times. Furthermore, for bosonic systems, we show that if the particle loss and particle gain rates are larger than the Gaussian intersite couplings, the system remains in a separable state at all times. Building on this characterization, we establish that at noise rates above a threshold, there exists a classical algorithm that can efficiently sample from the system state of both the fermionic and bosonic models. Finally, we show that, unlike fermionic systems, bosonic systems can evolve into states that are not convex Gaussian even when the dissipation is much higher than the on-site non-Gaussianity. Similarly, unlike bosonic systems, fermionic systems can generate entanglement even with noise rates much larger than the intersite couplings. 

Nuclear spins of noble gases exhibit exceptionally long coherence times and can potentially serve as a long-lived storage medium for quantum information. We analyze and compare the performance of two mechanisms for mapping the quantum state of light onto the collective spin state of noble gases. The first mechanism utilizes collisional exchange with the electronic spin state of metastable noble-gas atoms, while the second relies on spin-exchange collisions with ground-state alkali-metal atoms. We describe the operation of an optical quantum memory relying on these two mechanisms using a compact model and study strategies that optimize the memory storage efficiency. Through numerical simulations, we identify optimal sequences for storing optical signals with different signal bandwidths and electronic spin relaxation rates. This work highlights the qualitative difference between the two approaches for using noble gases as long-lived quantum memories at noncryogenic conditions and outlines the regimes in which they are expected to be efficient. 

To implement arbitrary quantum circuits in architectures with restricted interactions, one may effectively simulate all-to-all connectivity by routing quantum information. We consider the entanglement dynamics and routing between two regions only connected through an intermediate “bottleneck” region with few qubits. In such systems, where the entanglement rate is restricted by a vertex boundary rather than an edge boundary of the underlying interaction graph, existing results such as the small incremental entangling theorem give only a trivial constant lower bound on the routing time (the minimum time to perform an arbitrary permutation). We significantly improve the lower bound on the routing time in systems with a vertex bottleneck. Specifically, for any system with two regions $L,R$ with $N_L,N_R$ qubits, respectively, coupled only through an intermediate region $C$ with $N_C$ qubits, for any $\delta >0$ we show a lower bound of $\mathrm{\Omega }(N_R^{1-\delta }/\sqrt{N_L}{N}_C)$ on the Hamiltonian quantum routing time when using piecewise time-independent Hamiltonians, or time-dependent Hamiltonians subject to a smoothness condition. We also prove an upper bound on the average amount of bipartite entanglement between $L$ and $C,R$ that can be generated in time $t$ by such architecture-respecting Hamiltonians in systems constrained by vertex bottlenecks, improving the scaling in the system size from $O\left(N_{L}t\right)$ to $O\left(\sqrt{N_L}t\right)$ . As a special case, when applied to the star graph (i.e., one vertex connected to $N$ leaves), we obtain an $\mathrm{\Omega }\left(\sqrt{N^{1-\delta }}\right)$ lower bound on the routing time and on the time to prepare $N/2$ Bell pairs between the vertices. We also show that, in systems of free particles, we can route optimally on the star graph in time $\mathrm{\Theta }\left(\sqrt{N}\right)$ using Hamiltonian quantum routing, obtaining a speedup over gate-based routing, which takes time $\mathrm{\Theta }\left(N\right)$ . 

Recently, many experiments have been conducted with the goal of demonstrating a quantum advantage over classical computation. One popular framework for these experiments is Gaussian boson sampling, where quadratic photonic input states are interfered via a linear optical unitary and subsequently measured in the Fock basis. In this paper, we study the modal entanglement of the output states in this framework just before the measurement stage. Specifically, we compute Page curves as measured by various Rényi- $\alpha$ entropies, where the Page curve describes the entanglement between two partitioned groups of output modes averaged over all linear optical unitaries. We derive these formulas for $\alpha =1$ (i.e., the von Neumann entropy) and, more generally, for all positive integer $\alpha$ , in the asymptotic limit of infinite number of modes and for input states that are composed of single-mode-squeezed-vacuum state with equal squeezing strength. We then analyze the limiting behaviors when the squeezing is small and large. Having determined the averages, we then explicitly calculate the Rényi- $\alpha$ variance for integers $\alpha >1$ and are able to show that these entropies are weakly typical. Published by the American Physical Society2025