Ancilla-induced amplification of quantum Fisher information
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THE EUROPEAN PHYSICAL JOURNAL PLUS
Regular Article
Ancilla-induced amplification of quantum Fisher information C.S. Sudheer Kumar1,a and T.S. Mahesh2 1 2
Department of Physics and NMR Research Center, Indian Institute of Science Education and Research, Pune 411008, India Department of Physics and NMR Research Center, Center for Energy Sciences, Indian Institute of Science Education and Research, Pune 411008, India Received: 16 June 2018 / Revised: 25 August 2018 Published online: 12 November 2018 c Societ` a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2018 Abstract. Given a quantum state with an unknown parameter being measured with a suitable observable, Quantum Fisher Information (QFI) is the amount of information that one can extract about the unknown parameter. QFI also quantifies the maximum achievable precision in estimating the unknown parameter with a given amount of resource via quantum Cramer-Rao bound. In this work, we describe a protocol to amplify QFI of a single target qubit precorrelated with a set of ancillary qubits. Using an NMR system as an example, we show that a single quadrature NMR signal of only ancillary qubits suffices to perform the quantum state tomography (QST) of target qubit’s deviation part of the density matrix. We experimentally demonstrate this protocol using a star-topology spin-system consisting of a 13 C nuclear spin as the target qubit and three 1 H nuclear spins as ancillary qubits. We prepare the target qubit in various initial states, perform experimental QST, and estimate the amplification of QFI in each case. We also show that, in a high-temperature scenario like in the case of NMR, the QFI amplification scales linearly with the number of ancillary qubits and quadratically with the Bloch radius.
1 Introduction Quantum devices are expected to bring out a revolution in the way information is stored, manipulated, and communicated [1]. An important criterion to achieve this goal is the capability to efficiently measure two-level quantum systems, or qubits [2]. Spin-based systems are among various architectures which are being pursued for the physical realization of a quantum processor [3]. Nuclear spins in favorable atomic or molecular systems have the capability to store quantum information for sufficiently long durations and to allow precise implementation of desired quantum dynamics. Accordingly, nuclear magnetic resonance (NMR) is often considered as a convenient testbed for quantum emulations [4–6]. In a conventional NMR scheme, tiny nuclear polarizations demand a collective ensemble measurement of about 1015 identical spin-systems. There have been several proposals to increase the sensitivity of nuclear spin detection. For example, dynamic nuclear polarization (DNP) transfers polarization from electrons to nuclei, thereby enhancing the nuclear polarization up to three orders of magnitude [7]. Optical polarization and detection often enables single-spin measurements, such as in the case of nitrogen vacancy centers in diamond [8]. Further impro
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