Ancilla Assisted Quantum State Tomography in Many-Qubit Registers

TL;DR

This paper presents methods for implementing Ancilla Assisted Quantum State Tomography (AAQST) in multi-qubit systems and demonstrates its effectiveness through nuclear magnetic resonance experiments on two- and three-qubit registers.

Contribution

It introduces explicit construction methods for AAQST in many-qubit registers and validates them with experimental NMR studies.

Findings

AAQST reduces measurement complexity in multi-qubit systems.

Experimental validation confirms AAQST's effectiveness in NMR systems.

Single-experiment density matrix mapping achieved in multi-qubit registers.

Abstract

The standard method of Quantum State Tomography (QST) relies on the measurement of a set of noncommuting observables, realized in a series of independent experiments. Ancilla Assisted QST (AAQST) proposed by Nieuwenhuizen and co-workers (Phys. Rev. Lett., 92, 120402 (2004)) greatly reduces the number of independent measurements by exploiting an ancilla register in a known initial state. In suitable conditions AAQST allows mapping out density matrix of an input register in a single experiment. Here we describe methods for explicit construction of AAQST experiments in multi-qubit registers. We also report nuclear magnetic resonance studies on AAQST of (i) a two- qubit input register using a one-qubit ancilla in an isotropic liquid-state system and (ii) a three-qubit input register using a two-qubit ancilla register in a partially oriented system. The experimental results confirm the effectiveness of AAQST in such many-qubit registers.