Quantum-process tomography: Resource analysis of different strategies (original) (raw)

Ancilla-less selective and efficient quantum process tomography

2011

Several methods, known as Quantum Process Tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we present the theory describing a new type of method for quantum process tomography. We describe an algorithm that can be used to selectively estimate any parameter characterizing a quantum process. Unlike any of its predecessors this new quantum tomographer combines two main virtues: it requires investing a number of physical resources scaling polynomially with the number of qubits and at the same time it does not require any ancillary resources. We present the results of the first photonic implementation of this quantum device, characterizing quantum processes affecting two qubits encoded in heralded single photons. Even for this small system our method displays clear advantages over the other existing ones.

Selective and efficient quantum process tomography

Physical Review A, 2009

We present the results of the first photonic implementation of a new method for quantum process tomography. The method (originally presented by A. Bendersky et al, Phys. Rev. Lett 100, 190403 (2008)) enables the estimation of any element of the chi-matrix that characterizes a quantum process using resources that scale polynomially with the number of qubits. It is based on the idea of mapping the estimation of any chi-matrix element onto the average fidelity of a quantum channel and estimating the latter by sampling randomly over a special set of states called a 2-design. With a heralded single photon source we fully implement such algorithm and perform process tomography on a number of channels affecting the polarization qubit. The method is compared with other existing ones and its advantages are discussed.

Single-scan quantum process tomography

Physical Review A, 2014

The standard procedure for quantum process tomography (QPT) involves applying the quantum process on a system initialized in each of a complete set of orthonormal states. The corresponding outputs are then characterized by quantum state tomography (QST), which itself requires the measurement of non-commuting observables realized by independent experiments on identically prepared system states. Thus QPT procedure demands a number of independent measurements, and moreover, this number increases rapidly with the size of the system. However, the total number of independent measurements can be greatly reduced with the availability of ancilla qubits. Ancilla assisted process tomography (AAPT) has earlier been shown to require a single QST of system-ancilla space. Ancilla assisted quantum state tomography (AAQST) has also been shown to perform QST in a single measurement. Here we combine AAPT with AAQST to realize a 'single-shot QPT' (SSPT), a procedure to characterize a general quantum process in a single collective measurement of a set of commuting observables. We demonstrate experimental SSPT by characterizing several single-qubit processes using a three-qubit NMR quantum register. Furthermore, using the SSPT procedure we experimentally characterize the twirling process and compare the results with theory.

Direct Characterization of Quantum Dynamics

Physical Review Letters, 2006

The characterization of quantum dynamics is a fundamental and central task in quantum mechanics. This task is typically addressed by quantum process tomography (QPT). Here we present an alternative "direct characterization of quantum dynamics" (DCQD) algorithm. In contrast to all known QPT methods, this algorithm relies on error-detection techniques and does not require any quantum state tomography. We illustrate that, by construction, the DCQD algorithm can be applied to the task of obtaining partial information about quantum dynamics. Furthermore, we argue that the DCQD algorithm is experimentally implementable in a variety of prominent quantum information processing systems, and show how it can be realized in photonic systems with present day technology.

Limitations of quantum process tomography

2005

abstract Quantum process tomography is often cited as providing all the information that can be known about a given quantum process. In this paper we have shown that even if two processes appear identical under process tomography, it is possible to distinguish them using an interferometric setup. Using this setup, it is possible to gain more information about a process than just tomography provides.

How state preparation can affect a quantum experiment: Quantum process tomography for open systems

Physical Review A, 2007

We study the effects of preparation of input states in a quantum tomography experiment. We show that maps arising from a quantum process tomography experiment (called process maps) differ from the well know dynamical maps. The difference between the two is due to the preparation procedure that is necessary for any quantum experiment. We study two preparation procedures, stochastic preparation and preparation by measurements. The stochastic preparation procedure yields process maps that are linear, while the preparations using von Neumann measurements lead to non-linear processes, and can only be consistently described by a bi-linear process map. A new process tomography recipe is derived for preparation by measurement for qubits. The difference between the two methods is analyzed in terms of a quantum process tomography experiment. A verification protocol is proposed to differentiate between linear processes and bi-linear processes. We also emphasize the preparation procedure will have a non-trivial effect for any quantum experiment in which the system of interest interacts with its environment.

Selective and efficient quantum state tomography and its application to quantum process tomography

Physical Review A, 2013

We present a method for quantum state tomography that enables the efficient estimation, with fixed precision, of any of the matrix elements of the density matrix of a state, provided that the states from the basis in which the matrix is written can be efficiently prepared in a controlled manner. Furthermore, we show how this algorithm is well suited for quantum process tomography, enabling to perform selective and efficient quantum process tomography.

Quantum-enhanced tomography of unitary processes

Optica, 2015

A fundamental task in photonics is to characterise an unknown optical process, defined by properties such as birefringence, spectral response, thickness and flatness. Amongst many ways to achieve this, single-photon probes can be used in a method called quantum process tomography (QPT). Furthermore, QPT is an essential method in determining how a process acts on quantum mechanical states. For example for quantum technology, QPT is used to characterise multi-qubit processors 1 and quantum communication channels 2 ; across quantum physics QPT of some form is often the first experimental investigation of a new physical process, as shown in the recent research into coherent transport in biological mechanisms 3 . However, the precision of QPT is limited by the fact that measurements with single-particle probes are subject to unavoidable shot noise-this holds for both single photon and laser probes. In situations where measurement resources are limited, for example, where the process is rapidly changing or the time bandwidth is constrained, it becomes essential to overcome this precision limit. Here we devise and demonstrate a scheme for tomography which exploits non-classical input states and quantum interferences; unlike previous QPT methods our scheme capitalises upon the possibility to use simultaneously multiple photons per mode. The efficiency-quantified by precision per photon used-scales with larger photonnumber input states. Our demonstration uses fourphoton states and our results show a substantial reduction of statistical fluctuations compared to traditional QPT methods-in the ideal case one four-photon probe state yields the same amount of statistical information as twelve single probe photons.

Process tomography via sequential measurements on a single quantum system

Physical Review A, 2015

We utilize a discrete (sequential) measurement protocol to investigate quantum process tomography of a single two-level quantum system, with an unknown initial state, undergoing Rabi oscillations. The ignorance of the dynamical parameters is encoded into a continuous-variable classical system which is coupled to the two-level quantum system via a generalized Hamiltonian. This combined estimate of the quantum state and dynamical parameters is updated by using the information obtained from sequential measurements on the quantum system and, after a sufficient waiting period, faithful state monitoring and parameter determination is obtained. Numerical evidence is used to demonstrate the convergence of the state estimate to the true state of the hybrid system.