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arXiv:2209.02753 · Physical Review A

Suppressing amplitude damping in trapped ions: Discrete weak measurements for a nonunitary probabilistic noise filter

A. Blanco, K. Birgitta Whaley, A. Bermúdez

Published May 16, 2023• 15 citations
arXivHTMLPDF

Abstract

The idea of exploiting maximally entangled states as a resource lies at the core of several modalities of quantum information processing, including secure quantum communication, quantum computation, and quantum sensing. However, due to imperfections during or after the entangling gates used to prepare such states, the amount of entanglement decreases and their quality as a resource gets degraded. We introduce a low-overhead protocol to reverse this degradation by partially filtering out a specific type of noise relevant to many quantum technologies. We present two trapped-ion schemes for the implementation of a nonunitary probabilistic filter against amplitude damping noise, which can protect any maximally entangled pair from spontaneous photon scattering during or after the two-qubit trapped-ion entangling gates. This filter can be understood as a protocol for single-copy quasidistillation, as it uses only local operations to realize a reversal operation that can be understood in terms of weak measurements.

DOI
10.1103/physreva.107.052409

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The idea of exploiting maximally entangled states as a resource lies at the core of several modalities of quantum information processing, including secure quantum communication, quantum computation, and quantum sensing. However, due to imperfections during or after the entangling gates used to prepare such states, the amount of entanglement decreases and their quality as a resource gets degraded. We introduce a low-overhead protocol to reverse this degradation by partially filtering out a specific type of noise relevant to many quantum technologies. We present two trapped-ion schemes for the implementation of a nonunitary probabilistic filter against amplitude damping noise, which can protect any maximally entangled pair from spontaneous photon scattering during or after the two-qubit trapped-ion entangling gates. This filter can be understood as a protocol for single-copy quasidistillation, as it uses only local operations to realize a reversal operation that can be understood in terms of weak measurements.
Quantum entanglement is a critical resource for quantum information and quantum computation. However, entanglement of a quantum system is subjected to change due to the interaction with the environment. One typical result of the interaction is the amplitude damping that usually results in the reduction of the entanglement. Here we propose a protocol to protect quantum entanglement from the amplitude damping by applying Hadamard and CNOT gates. As opposed to some recently studied methods, the scheme presented here does not require weak measurement in the reversal process, leading to a faster recovery of entanglement. We propose a possible experimental implementation based on linear optical system.
Quantum entanglement is a critical resource for quantum information and quantum computation. However, entanglement of a quantum system is subjected to change due to the interaction with the environment. One typical result of the interaction is the amplitude damping that usually results in the reduction of the entanglement. Here we propose a protocol to protect quantum entanglement from the amplitude damping by applying Hadamard and CNOT gates. As opposed to some recently studied methods, the scheme presented here does not require weak measurement in the reversal process, leading to a faster recovery of entanglement. We propose a possible experimental implementation based on linear optical system.
Abstract Any kind of quantum resource useful in different information processing tasks is vulnerable to several types of environmental noise. Here we study the behaviour of quantum correlations such as entanglement and steering in two-qubit systems under the application of the generalised amplitude damping channel and propose two protocols towards preserving them under this type of noise. First, we employ the technique of weak measurement and reversal for the purpose of preservation of correlations. We then show how the evolution under the channel action can be seen as an unitary process. We use the technique of weak measurement and most general form of selective positive operator valued measure (POVM) to achieve preservation of correlations for a significantly large range of parameter values.
Being able to implement effective entanglement distribution in noisy environments is a key step towards practical quantum communication, and long-term efforts have been made on the development of it. Recently, it has been found that the null-result weak measurement (NRWM) can be used to enhance probabilistically the entanglement of a single copy of amplitude-damped entangled state. This paper investigates remote distributions of bipartite and multipartite entangled states in the amplitudedamping environment by combining NRWMs and entanglement distillation protocols (EDPs). We show that the NRWM has no positive effect on the distribution of bipartite maximally entangled states and multipartite Greenberger-Horne-Zeilinger states, although it is able to increase the amount of entanglement of each source state (noisy entangled state) of EDPs with a certain probability. However, we find that the NRWM would contribute to remote distributions of multipartite W states. We demonstrate that the NRWM can not only reduce the fidelity thresholds for distillability of decohered W states, but also raise the distillation efficiencies of W states. Our results suggest a new idea for quantifying the ability of a local filtering operation in protecting entanglement from decoherence.
Remote entanglement will inevitably decrease due to the interactions between quantum systems and their environments. Therefore protecting remote entanglement against decoherence is of great importance in realizing quantum communication and quantum comp utation. In this paper, we demonstrate that decoherence caused by weak-measurement-induced damping can be effectively suppressed by adding local unitary operation series on each qubit. The results show that the entanglement of the output state can approach that of the state before amplitude damping. The most distinct advantage of this entanglement protection scheme is that any unitary operation (except the identity operation) has this entanglement reversal effect on the amplitude-damped states. Furthermore, in each local unitary operation series, all the operations can be different from one other, and all the time intervals between any two adjacent operations can be different too. In addition, there is no need for the two remote users to synchronize their operations. Unlike most of the previous schemes, we do not assume the instantaneous local unitary operation, and each operation has a duration. All these advantages suggest that this remote entanglement protection scheme is much simpler and feasible than the previous ones, and we hope it can be implemented in the near future. Recently, Y. S. Kim et al. [Nat. Phys. 8, 117 (2012)] pointed out that ``pre-weak measurement +++ amplitude damping +++ bit-flipping operation +++ post-weak measurement'' can actively combat specific decoherence. By combing our proposal with Kim et al.'s scheme, the protection performance can be greatly improved by replacing the bit-flipping operation with an arbitrary rotational operation around the xxx axis, the number of the operations as well as the interval between any two adjacent operations all can be different, and the application range of the scheme can be greatly broadened.
Effectively managing various types of decoherence is crucial for leveraging entanglement in quantum information processing and quantum computing. In this paper, we propose purification circuits that deterministically produce a maximally entangled state from a single copy of an imperfect entangled pair affected by various noise sources. Unlike conventional methods, our approach eliminates the need for multiple copies of the entangled state, pre-purification operations, and imposes no restrictions on the initial entanglement fidelity of the imperfect pair. Our method utilizes ancilla qubits and CNOT gates to address errors from Pauli X and Z (bit flip and phase flip), as well as combinations of these errors that create general mixed entangled states and amplitude-damped entangled states. Our analysis shows that noisy CNOT gates impact fidelity minimally, with only the final two gates being critical. We validate our approach through mathematical analysis and practical implementation in Qiskit, demonstrating its effectiveness and robustness.