Determining ann-qubit state by a single apparatus through a pairwise interaction

Abstract

This paper shows how one can reconstruct an unknown n-qubit state by only a single apparatus. Its core is a redistribution of the information within an extended Hilbert space by coupling the unknown system with an assistant system through only a pairwise interaction, which results in a one-to-one mapping between the unknown density matrix elements and the probabilities of the occurrence of the eigenvalues of a single, factorized observable of the composite system. In such an interaction configuration, which is more feasible in experiments, the quality of the measurement only depends on that of the subsystem consisting a of one-qubit system coupled to a one-qubit assistant. We analyze in detail the performance of this procedure and experimentally implement it for reconstructing an unknown two-qubit state using a four-nuclear-spin system.

Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs

“…Estimating the quantum state of a quantum computer is an essential task to evaluate the performance of quantum algorithms [11], [12]. A d-dimensional quantum state is identified by a density operator, characterized by d 2 − 1 real parameters, which are estimated using quantum state tomography methods [13], [14] such as standard state tomography [12], using universal single observables [15]- [17], machine learning techniques [18], [19], or more recent classical shadow methods [20], [21]. This process is described using a measurement model [22], characterized by a set of positive operator-valued measurement (POVM) elements, which are operators that describe the statistics of the measurement process.…”

“…To study the estimation error for different initial states, in Fig. 3, we graphed the Fisher error (17) as a function of α 1 and α 2 . The parameters Θ 1 and Θ 2 where randomly chosen while Θ * represents the optimal parameters.…”

Hybrid direct state tomography by weak value

“…The unknown quantum state can not be perfectly cloned and determined by measuring only one quantum system [1]. In quantum information theory, quantum state tomography (QST) which is used to reconstruct the unknown state by measuring the identical quantum systems is an important topic [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In the conventional QST, it requires the measurements of a complete set of noncommutative observables, which are difficult to be realized perfectly in actual experiments, especially for highdimensional systems.…”

Direct state reconstruction with coupling-deformed pointer observables

“…Though the quantum no-clone theorem prohibits the perfect estimation of the unknown state of a single quantum system [1,2], state reconstruction is possible via repeatedly measuring an ensemble of identical systems, a process usually called quantum state tomography (QST). Besides the standard QST strategies [3][4][5][6][7][8][9][10], a novel tomography strategy, conventionally called direct state tomography (DST), or weak-value tomography, has been widely investigated both theoretically and experimentally [11][12][13][14][15][16][17][18][19].…”