Superior memory efficiency of quantum devices for the simulation of continuous-time stochastic processes

Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of information about past behaviour, even for relatively simple models, enforcing limits on precision due to the finite memory of the machine. However, quantum machines can require less information about the past than even their optimal classical counterparts to simulate the future of discrete-time processes, and we demonstrate that this advantage extends to the continuous-time regime. Moreover, we show that this reduction in the memory requirement can be unboundedly large, allowing for arbitrary precision even with a finite quantum memory. We provide a systematic method for finding superior quantum constructions, and a protocol for analogue simulation of continuous-time renewal processes with a quantum machine.Comment: 13 pages, 8 figures, title changed from original versio

A practical, unitary simulator for non-Markovian complex processes

Stochastic processes are as ubiquitous throughout the quantitative sciences as they are notorious for being difficult to simulate and predict. In this letter we propose a unitary quantum simulator for discrete-time stochastic processes which requires less internal memory than any classical analogue throughout the simulation. The simulator's internal memory requirements equal those of the best previous quantum models. However, in contrast to previous models it only requires a (small) finite-dimensional Hilbert space. Moreover, since the simulator operates unitarily throughout, it avoids any unnecessary information loss. We provide a stepwise construction for simulators for a large class of stochastic processes hence directly opening the possibility for experimental implementations with current platforms for quantum computation. The results are illustrated for an example process.Comment: 12 pages, 5 figure

Unified framework for quantumness -- coherence, discord, and entanglement

From an operational perspective, quantumness characterizes the exotic behavior in a physical process which cannot be explained with Newtonian physics. There are several widely used measures of quantumness, including coherence, discord, and entanglement, each proven to be essential resources in particular situations. There exists evidence of fundamental connections amongst the three measures. However, those quantumnesses are still regarded differently and such connections are yet to be elucidated. Here, we introduce a general framework of defining a unified quantumness with an operational motivation founded on the capability of interferometry. The quantumness appears differently as coherence, discord, and entanglement in different scenarios with local measurement, weak reference frame free measurement, and strong reference frame free measurement, respectively. Our results also elaborate how these three measures are related and how they can be transformed from each other. This framework can be further extended to other scenarios and serves as a universal quantumness measure.Comment: 9 pages, 4 figure

Unconditional preparation of entanglement between atoms in cascaded optical cavities

We propose a scheme to unconditionally entangle the internal states of atoms trapped in separate high finesse optical cavities. The scheme uses the technique of quantum reservoir engineering in a cascaded cavity QED setting, and for ideal (lossless) coupling between the cavities generates an entangled pure state. Highly entangled states are also shown to be possible for realizable cavity QED parameters and with nonideal coupling.Comment: 4 pages, 5 figures, submitted to Physical Revie