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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Deterministic purity evolution via weak measurement for bipartite quantum systems

Charles D. Hill, Jason F. Ralph

Published Jun 7, 2007• 0 citations
Publisher

Abstract

In this paper we consider feedback control algorithms for the deterministic purification of a bipartite state consisting of two qubits, when the observer has access to only one of the qubits. We show that Hamiltonian feedback control can be used to produce deterministic evolution of the purity of either qubit individually, or both together.

DOI
10.1117/12.724659

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Scientific Reports•Dec 27, 2022•2 citations
In this paper we consider feedback control algorithms for the deterministic purification of a bipartite state consisting of two qubits, when the observer has access to only one of the qubits. We show that Hamiltonian feedback control can be used to produce deterministic evolution of the purity of either qubit individually, or both together.
In this paper, we consider feedback control algorithms for the rapid purification of a bipartite state consisting of two qubits, when the observer has access to only one of the qubits. We show (1) the algorithm maximizing the average purification rate is different from that for a projective measurement and (2) that the weak measurement protocol for bipartite systems contrasts with known single qubit protocols. We also reveal that the rate of increase in purity may be made deterministic for bipartite states.
In this paper we show how weak measurement and local feedback can be used to control entanglement generation between two qubits. To do this, we make use of a decoherence free subspace. Weak measurement and feedback can be used to drive the system into this subspace rapidly. Once within the subspace, feedback can generate entanglement rapidly, or turn off entanglement generation dynamically. We also consider, in the context of weak measurement, some of the differences between purification and generating entanglement.
This paper reconsiders the claimed rapidity of a scheme for the purification of the quantum state of a qubit, proposed recently in Jacobs (2003 Phys. Rev. A 67 030301(R)). The qubit starts in a completely mixed state, and information is obtained by a continuous measurement. Jacobs' rapid purification protocol uses Hamiltonian feedback control to maximize the average purity of the qubit for a given time , with a factor of two increase in the purification rate over the no-feedback protocol. However, by re-examining the latter approach, we show that it minimizes the average time taken for a qubit to reach a given purity . In fact, the average time taken for the no-feedback protocol beats that for Jacobs' protocol by a factor of two. We discuss how this is compatible with Jacobs' result and the usefulness of the different approaches.
We investigate assisted enhancement of quantum coherence in a bipartite setting with control and target systems, which converts the coherence of the control qubit into the enhanced coherence of the target qubit. We assume that only incoherent operations and measurements can be applied locally and classical information can be exchanged. In addition, the two subsystems are also coupled by a fixed Hamiltonian whose interaction strength can be controlled. This coupling does not generate any local coherence from incoherent input states. We show that in this setting a measurement and feed-forward based protocol can deterministically enhance the coherence of the target system while fully preserving its purity. The protocol can be iterated and several copies of the control state can be consumed to drive the target system arbitrarily close to a maximally coherent state. We experimentally demonstrate this protocol with a photonic setup and observe the enhancement of coherence for up to five iterations of the protocol.