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arXiv:1610.06854 · Journal of the Optical Society of America B

Probing single-photon state tomography using phase-randomized coherent states

Paulo Valente, A. Lezama

Published Apr 10, 2017• 10 citations
arXivHTMLPDF

Abstract

Quantum processes involving single-photon states are of broad interest, in particular, for quantum communications. Extending to continuous values a recent proposal by Yuan et al. [Phys. Rev. A94, 062305 (2016)PLRAAN1050-294710.1103/PhysRevA.94.062305], we show that single-photon quantum processes can be characterized using phase-randomized coherent states (PRCS) as inputs. As a proof of principle, we present the experimental investigation of single-photon tomography using PRCS. The probability distribution of field quadrature measurements for single-photon states can be accurately derived from the PRCS data. As a consequence, the Wigner function and the density matrix of single-photon states are reconstructed with good precision. The sensitivity of the reconstruction to experimental errors and the number of PRCS used is addressed.

DOI
10.1364/josab.34.000924

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Quantum processes involving single-photon states are of broad interest, in particular, for quantum communications. Extending to continuous values a recent proposal by Yuan et al. [Phys. Rev. A94, 062305 (2016)PLRAAN1050-294710.1103/PhysRevA.94.062305], we show that single-photon quantum processes can be characterized using phase-randomized coherent states (PRCS) as inputs. As a proof of principle, we present the experimental investigation of single-photon tomography using PRCS. The probability distribution of field quadrature measurements for single-photon states can be accurately derived from the PRCS data. As a consequence, the Wigner function and the density matrix of single-photon states are reconstructed with good precision. The sensitivity of the reconstruction to experimental errors and the number of PRCS used is addressed.
We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state 1> was prepared using conditional measurements on photon pairs born in the process of parametric down-conversion. A probability distribution of the phase-averaged electric field amplitudes with a strongly non-Gaussian shape is obtained with the total detection efficiency of (55+/-1)%. The angle-averaged Wigner function reconstructed from this distribution shows a strong dip reaching classically impossible negative values around the origin of the phase space.
Quantum state engineering and state characterization is a key task in quantum information processing in both discrete and continuous variable systems in the optical domain. In particular, quantum states with non-Gaussian (i.e., non-positive) Wigner quasiprobability distribution functions are crucial to universal, fault-tolerant quantum computing with continuous variables. In this talk, we present our recent results on single-photon Fock state tomography using Photon-Number-Resolving (PNR) measurements. We generated a highly pure narrow-band single-photon Fock state by heralding cavity-enhanced spontaneous-parametric-downconversion from a PPKTP optical parametric oscillator. The Wigner function was reconstructed with photon statistics obtained using superconducting transition-edge sensors with an overall system efficiency of 58(2)%. We then discuss quantum state engineering for pure displaced single-photon Fock states, optical cat states, and approximate GKP states using coherent states and single-photon states along with linear optics and PNR measurements. We report our experimental progress for the same.
In a recently demonstrated quantum-state tomography scheme [P. Yang, M. Yu, R. Betzholz, C. Arenz, and J. Cai, Phys. Rev. Lett. 124, 010405 (2020)], a random-control field is locally applied to a multipartite system to reconstruct the full quantum state of the system through single-observable measurements. Here, we analyze the robustness of such a tomography scheme against measurement errors. We characterize the sensitivity to measurement errors using the condition number of a linear system that fully describes the tomography process. Using results from random matrix theory we derive the scaling law of the logarithm of this condition number with respect to the system size when Haar-random evolutions are considered. While this expression is independent of how Haar randomness is created, we also perform numerical simulations to investigate the temporal behavior of the robustness for two specific quantum systems that are driven by a single random-control field. Interestingly, we find that before the mean value of the logarithm of the condition number as a function of the driving time asymptotically approaches the value predicted for a Haar-random evolution it reaches a plateau whose length increases with the system size.
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 and quantum communication channels; 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. 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 photon number input states. Our demonstration uses four-photon 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.
We propose a model for the quantum-state measurement via phase-sensitive amplification. The basic idea is to amplify the quantum state through a two-photon correlated-emission laser, such that there is no noise in the quadrature of interest and all the noise is fed into the conjugate quadrature. The noise-free quadrature is prepared in different phases and then corresponding quadrature distribution is measured. The Wigner function of the initial quantum state is then reconstructed by carrying out inverse Radon transformation familiar in tomographic imaging. This scheme allows us to avoid the deterioration of homodyne detection measurement due to the problem of detector efficiency.
Experiments have been performed to determine the Wigner distribution and the density matrix (and for pure states the wave function) of a light mode, by using tomographic inversion of a set of measured probability distributions for quadrature amplitudes.From these measurements the quantum distributions of optical phase and photon number have been obtained.The measurements of quadrature-amplitude distributions for a temporal mode of the electromagnetic field are carried out using balanced homodyne detection.We refer to this new method as optical homodyne tomography.Given the measured density matrix, one can experimentally infer any of the various quantum distributions of optical phase, in particular the Pegg-Barnett (or, equivalently, Shapiro-Shepard) phase distribution, the marginal Wigner distribution, and the Vogel-Schleich operational phase distribntion.We have used this approach to make measurements of the number-plase uncertainty relation for coherent-state fields.The coherent states do not attain the minimum value for the number-phase uncertainty product, as set by the expectation value of the commutator of the number and phase operators; this is true theoretically and experimentally.