Preservation of a lower bound of quantum secret key rate in the presence of decoherence

Abstract

It is well known that the interaction of quantum systems with the environment reduces the inherent quantum correlations. Under special circumstances the effect of decoherence can be reversed, for example, the interaction modeled by an amplitude damping channel can boost the teleportation fidelity from the classical to the quantum region for a bipartite quantum state. Here, we first show that this phenomena fails in the case of a quantum key distribution protocol. We further show that the technique of weak measurement can be used to slow down the process of decoherence, thereby helping to preserve the quantum key rate when one or both systems are interacting with the environment via an amplitude damping channel. Most interestingly, in certain cases weak measurement with post-selection where one considers both success and failure of the technique is shown to be more useful than without it when both systems interact with the environment.

Preservation of quantum nonbilocal correlations in noisy entanglement-swapping experiments using weak measurements

“…We employ the technique of weak measurement and its reversal which has been known to preserve certain other types of quantum correlations [23][24][25] against the effect of decoherence. Here, weak measurement is performed by the central party, which helps to slow down the effect of amplitude damping on the state when the particles are transmitted to the two other parties.…”

“…A promising avenue in this direction is provided by weak measurements [20] which are based on weak coupling between the system and the measurement device, and have interesting applications in different arenas such as demonstration of spin Hall effect [21] and wave-particle duality [22]. Weak measurements have been employed to protect quantumness of bipartite systems used in several applications such as generation of entanglement [23], enhancement of teleportation fidelity [24], and protection of the secret key rate in one-sided device independent QKD [25]. The technique of weak measurement and its reversal has been used to preserve correlations in quantum states transmitting through amplitude damping channels (ADC).…”

“…The above expression is obtained for the optimal choice of measurement settings for Alice, Bob and Charlie, given by, a Fig.2 illustrates that as number of interaction with the environment increases, the amount of quantum nonbilocality reduces in the system. It may be noted that unlike the case of teleportation fidelity [18,19], quantum non-bilocality resembles the behaviour of the lower bound of quantum secret key rate in one-sided device independent quantum key distribution(1s-DIQKD) [25], where classical correlation plays no role in improving the relevant measure under decoherence.…”

A historical review and Bibliometric analysis of research on Weak measurement research over the past decades based on Biblioshiny

“…Quantum decoherence plays a pivotal role in the dynamical description of the quantum-to-classical transition and is the main impediment to the realization of devices for quantum information processing. Recently, weak measurements, which consist of several positive operators valued measures are performed before or after the evolution of the quantum system to reduce the decoherence of the system caused by the environment [53][54][55][56]. Datta et al [53] demonstrated that the technique of weak measurement can be used to slow down the process of decoherence, thereby helping to preserve the quantum secret key rate when one or both systems are interacting with the environment via an amplitude damping channel.…”

“…Recently, weak measurements, which consist of several positive operators valued measures are performed before or after the evolution of the quantum system to reduce the decoherence of the system caused by the environment [53][54][55][56]. Datta et al [53] demonstrated that the technique of weak measurement can be used to slow down the process of decoherence, thereby helping to preserve the quantum secret key rate when one or both systems are interacting with the environment via an amplitude damping channel. Pramanik et al [54] employed the technique of weak measurement to enable the preservation of teleportation fidelity for two-qubit noisy channels.…”