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arXiv:2404.11175 · Physical Review A

Active quantum distillation

Muchun Yang, D. L. Zhou

Published Jul 31, 2024• 1 citation
arXivHTMLPDF

Abstract

Quantum distillation is a modern technology to decrease the von Neumann entropy of a subsystem by coherent system dynamics. Here we propose an active quantum distillation protocol, in which a bang-bang theme is applied to actively control the coherent dynamics of our system in order to obtain a subsystem with the von Neumann entropy as low as possible. For a bipartite bosonic system, we derive the analytical expression of the entropy lower bound of one subsystem under any unitary transformation for mixed states with conservation of particles. The lower bound is validated by numerical simulations on the Bose-Hubbard model, where the coherent evolution is controlled by tuning one interaction term of the Hamiltonian. Our protocol can be used to decrease the entropy of one subsystem lower than the total bipartite state and increase the number of bosons or only distill out very few bosons in the subsystem.

DOI
10.1103/physreva.110.012622

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Quantum distillation is a modern technology to decrease the von Neumann entropy of a subsystem by coherent system dynamics. Here we propose an active quantum distillation protocol, in which a bang-bang theme is applied to actively control the coherent dynamics of our system in order to obtain a subsystem with the von Neumann entropy as low as possible. For a bipartite bosonic system, we derive the analytical expression of the entropy lower bound of one subsystem under any unitary transformation for mixed states with conservation of particles. The lower bound is validated by numerical simulations on the Bose-Hubbard model, where the coherent evolution is controlled by tuning one interaction term of the Hamiltonian. Our protocol can be used to decrease the entropy of one subsystem lower than the total bipartite state and increase the number of bosons or only distill out very few bosons in the subsystem.
We introduce and study the task of assisted coherence distillation. This task arises naturally in bipartite systems where both parties work together to generate the maximal possible coherence on one of the subsystems. Only incoherent operations are allowed on the target system, while general local quantum operations are permitted on the other; this is an operational paradigm that we call local quantum-incoherent operations and classical communication. We show that the asymptotic rate of assisted coherence distillation for pure states is equal to the coherence of assistance, an analog of the entanglement of assistance, whose properties we characterize. Our findings imply a novel interpretation of the von Neumann entropy: it quantifies the maximum amount of extra quantum coherence a system can gain when receiving assistance from a collaborative party. Our results are generalized to coherence localization in a multipartite setting and possible applications are discussed.
We obtain the general formula for the optimal rate on one of the subsystems that can be distilled from any bipartite quantum state by one-way local quantum-incoherent operations and classical communication. We provide lower and upper bounds on the assisted distillation of coherence using so-called one-shot entropies, and we establish a hierarchy of information quantities that can be used to calculate an assisted distillable rate in the asymptotical limit. We show that they asymptotically coincide with the quantum-incoherent relative entropy, and our findings imply a novel operational interpretation of quantum-incoherent relative entropy.
High-fidelity entanglement shared between distant quantum systems is an essential resource for quantum communication and computation. Entanglement distillation addresses this need by converting multiple noisy Bell pairs into fewer higher-fidelity pairs, using only local quantum operations and classical communication. However, this approach typically requires a substantial overhead in the number of qubits. To bypass this hurdle, we propose to leverage the high-dimensional Hilbert space of a single pair of bosonic systems to store a large amount of entanglement, replacing the need for multi-qubit systems. To distill entanglement in such a setup, we devise a new entanglement distillation protocol, tailored for bosonic systems. The protocol converts a highly-entangled noisy state between two bosonic systems into a lower-dimensional but high-fidelity entangled state, using only local bosonic operations. We show that our protocol significantly enhances the fidelity of the entangled state in the presence of naturally occurring loss and dephasing errors. Compared to methods relying on multiple Bell pairs, our scheme offers a more hardware-efficient strategy, providing a practical route toward the realization of entanglement distillation.
Efficient entanglement distribution is a cornerstone of the Quantum Internet. However, physical link parameters such as photon loss, memory coherence time, and gate error rates fluctuate dynamically, rendering static purification strategies suboptimal. In this paper, we propose an Adaptive Purification Controller (APC) that automatically optimizes the entanglement distillation sequence to maximize the goodput, i.e., the rate of delivered pairs meeting a strict fidelity threshold. By treating protocol selection as a resource allocation problem, the APC dynamically switches between purification depths and protocols (BBPSSW vs. DEJMPS) to navigate the trade-off between generation rate and state quality. Using a dynamic programming planner with Pareto pruning, simulation results show that our approach mitigates the "fidelity cliffs" inherent in static protocols and reduces resource wastage in high-noise regimes. Furthermore, we extend the controller to heterogeneous scenarios, and evaluate it for both multipartite GHZ state generation and continuous-variable systems using effective noiseless linear amplification models. We benchmark its computational overhead, showing decision latencies in the millisecond range per link in our implementation.
A model of discrete dynamics of entanglement of a bipartite quantum state is considered. It involves a global unitary dynamics of the system and periodic actions of local bistochastic or decaying channel. For initially pure states the decay of entanglement is accompanied by an increase of von Neumann entropy of the system. We observe and discuss revivals of entanglement due to unitary interaction of subsystems. For some mixed states having different marginal entropies of the subsystems we find an asymmetry in speed of entanglement decay. The entanglement of these states decreases faster, if the depolarizing channel acts on the ``classical'' subsystem, characterized by smaller marginal entropy.
We study the short-time evolution of the bipartite entanglement in quantum lattice systems with local interactions in terms of the purity of the reduced density matrix. A lower bound for the purity is derived in terms of the eigenvalue spread of the interaction Hamiltonian between the partitions. Starting from an initially separable state the purity decreases as $1\ensuremath{-}(t/\ensuremath{\tau}){}^{2}$ (i.e., quadratically in time, with a characteristic timescale $\ensuremath{\tau}$ that is inversely proportional to the boundary size of the subsystem, that is, as an area law). For larger times an exponential lower bound is derived corresponding to the well-known linear-in-time bound of the entanglement entropy. The validity of the derived lower bound is illustrated by comparison to the exact dynamics of a one-dimensional spin lattice system as well as a pair of coupled spin ladders obtained from numerical simulations.