Multiple phase estimation in quantum cloning machines
arXiv:1407.5748 · doi:10.1103/PhysRevA.90.022327
Abstract
Since the initial discovery of the Wootters-Zurek no-cloning theorem, a wide variety of quantum cloning machines have been proposed aiming at imperfect but optimal cloning of quantum states within its own context. Remarkably, most previous studies have employed the Bures fidelity or the Hilbert-Schmidt norm as the figure of merit to characterize the quality of the corresponding cloning scenarios. However, in many situations, what we truly care about is the relevant information about certain parameters encoded in quantum states. In this work, we investigate the multiple phase estimation problem in the framework of quantum cloning machines, from the perspective of quantum Fisher information matrix (QFIM). Focusing on the generalized d-dimensional equatorial states, we obtain the analytical formulas of QFIM for both universal quantum cloning machine (UQCM) and phase-covariant quantum cloning machine (PQCM), and prove that PQCM indeed performs better than UQCM in terms of QFIM. We highlight that our method can be generalized to arbitrary cloning schemes where the fidelity between the single-copy input and output states is input-state independent. Furthermore, the attainability of the quantum Cramer-Rao bound is also explicitly discussed.
10 pages, 3 figures. Any suggestions and comments are welcome!
References in corpus (48)
- Advances in Quantum Metrology
- Quantum-enhanced measurements: beating the standard quantum limit
- Quantum metrology
- Security of quantum key distribution using d-level systems
- Quantum Copying: Beyond the No-Cloning Theorem
- Remote State Preparation
- Optimal Quantum Cloning Machines
- Generalized uncertainty relations: Theory, examples, and Lorentz invariance
- Quantum cloning
- Optimal Universal and State-Dependent Quantum Cloning
- Probabilistic cloning and identification of linearly independent quantum states
- Quantum Enhanced Multiple Phase Estimation
- Phase covariant quantum cloning
- Optimal universal quantum cloning and state estimation
- Weak value amplification is suboptimal for estimation and detection
- A new approach to the Cramer-Rao type bound of the pure state model
- Quantum Fisher information of entangled coherent state in the presence of photon losses: exact solution
- Phase matching condition for enhancement of phase sensitivity in quantum metrology
- Optimal estimation of joint parameters in phase space
- A tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry
- When amplification with weak values fails to suppress technical noise
- Two qubit copying machine for economical quantum eavesdropping
- Quantum Fisher information for density matrices with arbitrary ranks
- Local asymptotic normality for finite dimensional quantum systems
- Quantum cloning machines for equatorial qubits
- Information amplification via postselection: A parameter estimation perspective
- Quantum Cloning Machines and the Applications
- Phase-covariant quantum cloning of qudits
- Optimal phase covariant cloning for qubits and qutrits
- Optimal Non-Universally Covariant Cloning
- Quantum limits on post-selected, probabilistic quantum metrology
- Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
- Economical Phase-Covariant Cloning of Qudits
- Optimal Measurement on Noisy Quantum Systems
- Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks
- Estimation of unitary quantum operations
- Optimal estimation of entanglement
- Local asymptotic normality in quantum statistics
- Quantum sensors based on weak-value amplification cannot overcome decoherence
- Economical quantum cloning in any dimension
- Information geometry of Gaussian channels
- Entanglement is not very useful for estimating multiple phases
- Optimal estimation of multiple phases
- Quantum estimation of a two-phase spin rotation
- Cloning a Qutrit
- Broadcasting Quantum Fisher Information
- Optimal quantum multi-parameter estimation and application to dipole- and exchange-coupled qubits
- Joint estimation of real squeezing and displacement
Cited by in corpus (16)
- Quantum Fisher information matrix and multiparameter estimation
- Multi-parameter Quantum Metrology
- Control-enhanced multiparameter quantum estimation
- Gaussian systems for quantum enhanced multiple phase estimation
- Quantum metrology with unitary parametrization processes
- Quantum multiparameter metrology with generalized entangled coherent state
- Enhancing parameter precision of optimal quantum estimation by direct quantum feedback
- Quantum Fisher information and symmetric logarithmic derivative via anti-commutators
- Multiple phase estimation for arbitrary pure states under white noise
- Coherence enhanced quantum metrology in a nonequilibrium optical molecule
- Optimal quantum parameter estimation in a pulsed quantum optomechanical system
- The energy level crossing behavior and quantum Fisher information in a quantum well with spin-orbit coupling
- Distribution of quantum Fisher information in asymmetric cloning machines
- Multi-parameter estimation with multi-mode Ramsey interferometry
- Quantum-phase synchronization
- High-precision estimation of the parameters in the reservoir via the two-level system