Quantum System Identification

Abstract

The aim of quantum system identification is to estimate the ingredients inside a black box, in which some quantum-mechanical unitary process takes place, by just looking at its input-output behavior. Here we establish a basic and general framework for quantum system identification, that allows us to classify how much knowledge about the quantum system is attainable, in principle, from a given experimental setup. We show that controllable closed quantum systems can be estimated up to unitary conjugation. Prior knowledge on some elements of the black box helps the system identification. We present an example in which a Bell measurement is more efficient to identify the system. When the topology of the system is known, the framework enables us to establish a general criterion for the estimability of the coupling constants in its Hamiltonian.

Dynamical phase transitions as a resource for quantum enhanced metrology

“…The estimation of unknown parameters is a crucial task for quantum technology applications such as state tomography [1], system identification [2], and quantum metrology [3][4][5]. Enhancement in precision can be achieved by using entangled (highly correlated) quantum states which encode the unknown parameter, like the Greenberger-Horne-Zeilinger (GHZ) state |GHZ = |0 ⊗N + |1 ⊗N constructed of N qubits.…”

“…,k are approximately block diagonal with respect to a splitting into some orthogonal subspaces H 1 and H 2 . For pure initial states |χ (1) , |χ (2) supported in these subspaces, the corresponding evolved states ρ (1) (t), ρ (2) (t) will thus stay supported approximately within H 1 , H 2 , respectively, for times t τ . Moreover, those states will be well approximated by linear combinations of ρ ss and ρ 2 for times τ t τ .…”

“…Moreover, those states will be well approximated by linear combinations of ρ ss and ρ 2 for times τ t τ . We now sketch how to define the orthogonal subspaces H 1 , H 2 , and the initial states |χ (1) , |χ (2) using the master operator L. Due to L preserving Hermiticity of matrices, λ 2 ∈ R and both ρ 2 and l 2 are Hermitian matrices on H; i.e., they diagonalize and their spectra are real. First, inspired by the form of the second eigenvector at a first-order DPT, l 2 = (1 − p)P H A − pP H I , we define the subspaces H 1 , H 2 in the following way.…”

“…H 1 is spanned by the eigenvectors of l 2 which correspond to positive eigenvalues close to the maximal eigenvalue of l 2 , while H 2 is spanned by eigenvectors of l 2 corresponding to negative eigenvalues close to the minimal eigenvalue of l 2 . Next, the initial states |χ (1) and |χ (2) are chosen to be the eigenvectors corresponding to maximal and minimal eigenvalue of l 2 , respectively. Finally, these states evolve into the states ρ (1) (t), ρ (2) (t) which are approximately stationary in the regime τ t τ and well approximated by linear combinations of ρ ss and ρ 2 [30].…”

Optimal design of measurement settings for quantum-state-tomography experiments

“…The problem of estimating an unknown quantum state is of fundamental importance in quantum physics [1] and especially in the field of quantum information processing, such as quantum computation [2], quantum cryptography [3], and quantum system identification [4]. Quantum state tomography aims to determine the full state of a quantum system via a series of quantum measurements.…”