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JSAP-OSA Joint Symposia

Multiparameter estimation with single photons—Linearly-optically generated quantum entanglement beats the shotnoise limit

Chenglong You, Sushovit Adhikari, Yuxi Chi, Margarite L. LaBorde, Corey T. Matyas, Chenyu Zhang, Zu-En Su, Tim Byrnes, Chao‐Yang Lu, Jonathan P. Dowling, Jonathan P. Olson

Published Jan 1, 2017• 4 citations
Publisher

Abstract

It was previously shown that optical networks using only single photon Fock states, passive linear optics, and single photon detection could achieve post-classical sensitivity for singleparameter estimation when the mode number is small. [1] Furthermore, it was shown that multiparameter estimation could achieve similar results with number-resolving detection. [2] Here, we consider an analogous architecture to the Quantum Fourier Transform Interferometer(QuFTI) proposed in [1] for the estimation of multiple phases simultaneously. Thus, we will see that this yields post-classical sensitivity for multiparameter estimation even for an asymptotically large number of modes. This system is also considered for nondeterministic photon sources and a variety of measurement schemes.

DOI
10.1364/jsap.2017.7p_a410_4

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It was previously shown that optical networks using only single photon Fock states, passive linear optics, and single photon detection could achieve post-classical sensitivity for singleparameter estimation when the mode number is small. [1] Furthermore, it was shown that multiparameter estimation could achieve similar results with number-resolving detection. [2] Here, we consider an analogous architecture to the Quantum Fourier Transform Interferometer(QuFTI) proposed in [1] for the estimation of multiple phases simultaneously. Thus, we will see that this yields post-classical sensitivity for multiparameter estimation even for an asymptotically large number of modes. This system is also considered for nondeterministic photon sources and a variety of measurement schemes.
Abstract It was suggested in (Motes et al 2015 Phys. Rev. Lett. 114 170802) that optical networks with relatively inexpensive overheads—single photon Fock states, passive optical elements, and single photon detection—can show significant improvements over classical strategies for single-parameter estimation, when the number of modes in the network is small ( n < 7 ). A similar case was made in (Humphreys et al 2013 Phys. Rev. Lett. 111 070403) for multi-parameter estimation, where measurement is instead made using photon-number resolving detectors. In this paper, we analytically compute the quantum Cramér–Rao bound to show these networks can have a constant-factor quantum advantage in multi-parameter estimation for even large number of modes. Additionally, we provide a simplified measurement scheme using only single-photon (on–off) detectors that is capable of approximately obtaining this sensitivity for a small number of modes.
Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation beyond what reachable within classical physics. While single parameter estimation theory has been widely investigated, much less is known about the simultaneous estimation of multiple phases, which finds key applications in imaging and sensing. In this manuscript we provide conditions of useful entanglement (among multimode particles, qudits) for multiphase estimation and adapt them to multiarm Mach-Zehnder interferometry. We discuss benchmark multimode Fock states containing useful qudit entanglement and overcoming the sensitivity of separable qudit states in three and four arm Mach-Zehnder-like interferometers - currently within the reach of integrated photonics technology.
Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation over that achievable by classical physics. While single parameter estimation theory has been widely investigated, much less is known about the simultaneous estimation of multiple phases, which finds key applications in imaging and sensing. In this manuscript we provide conditions of useful particle (qudit) entanglement for multiphase estimation and adapt them to multiarm Mach-Zehnder interferometry. We theoretically discuss benchmark multimode Fock states containing useful qudit entanglement and overcoming the sensitivity of separable qudit states in three and four arm Mach-Zehnder-like interferometers - currently within the reach of integrated photonics technology.
Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement has been thought to be resource intensive to create in the first place--typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feedforward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multiphoton walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer--fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection--is capable of significantly beating the shot-noise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.
Phase estimation has a wide range of applications. Over the years, several strategies have been studied to improve precision in phase estimation. These strategies include using exotic quantum states to quantum detection schemes. This dissertation summarizes my effort in improving the precision of phase estimation with a linear and nonlinear interferometer. Chapter 1 introduces quantum optics and quantum metrology. I introduce all relevant quantum states of light used. We also look into tools and terminologies of quantum metrology such as Fisher information, shot-noise limit, Heisenberg limit, etc., along with examples of phase estimation with a Mach-Zehnder interferometer. In Chapter 2, I discuss multiple phase estimation using a multimode interferometer. Building upon previous work, our scheme consists of a multimode interferometer with single-photon inputs. By using a quantum Fisher information analysis, we show that our scheme gives a constant improvement over other schemes. We also show that our scheme with photon-number-resolving detection approaches the quantum Cram\'er-Rao bound. Moreover, we also consider the probabilistic nature of photon emission at the input, and we study its effect on phase sensitivity. I discuss phase estimation with SU(1,1) interferometer in Chapter 3. We look at phase sensitivity in this interferometer with different input states. Namely, we consider two different phase estimation scheme, one using thermal and squeezed states, and others using coherent and displaced squeezed states with parity and on-off as a detection scheme. We also look into the effect of photon loss inside the interferometer. In Chapter 4, we revisit phase estimation in SU(1,1) interferometer from the perspective of quantum Fisher information. I discuss in detail a longstanding confusion regarding the use of quantum Fisher information in SU(1,1) interferometer. We show that phase averaging or quantum Fisher information matrix method is needed in general for calculating the phase sensitivity which resolves inconsistencies reported in previously published articles.