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Laser Physics

Improving quantum phase estimation via power-law potential systems

K. Berrada

Published Apr 30, 2014• 17 citations
Publisher

Abstract

Using the quantum Fisher information (QFI), we present an improved phase estimation scheme employing power-law potential (PLP) systems in comparison to NOON states under perfect and lossy conditions for a fixed mean photon number. The study is devoted to the phase estimation of the quantum states resulting from tightly binding, harmonic and loosely binding potentials for modest particle numbers. Finally, we discuss the saturation of the optimal phase uncertainty of this interferometric setting with parity detection.

DOI
10.1088/1054-660x/24/6/065201

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Using the quantum Fisher information (QFI), we present an improved phase estimation scheme employing power-law potential (PLP) systems in comparison to NOON states under perfect and lossy conditions for a fixed mean photon number. The study is devoted to the phase estimation of the quantum states resulting from tightly binding, harmonic and loosely binding potentials for modest particle numbers. Finally, we discuss the saturation of the optimal phase uncertainty of this interferometric setting with parity detection.
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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.
Abstract In this work we address the optimization of two important quantum states in terms of interferometric phase sensitivity, given a constraint on the total average number of input photons, N ¯ We use the quantum Fisher information (QFI) as our main tool. We employ both the single- and two-parameter QFI in order to address detection schemes having, and respectively, not having access to an external phase reference. The first quantum state we consider is the coherent plus squeezed vacuum input and find the optimum coherent fraction that maximizes both the single- and two-parameter QFI. We also discuss detection schemes able to perform almost optimally. Finally, we consider the double squeezed vacuum input and determine the squeezed fraction between the inputs that maximizes the QFI. Similar to the previous input state, we also provide detection schemes able to perform optimally.
Abstract The enhancement of the precision of phase estimation in quantum metrology is investigated by employing parity-time ( P T ) symmetric operation. We derive the exact expressions of the quantum Fisher information (QFI) and the success probability of the phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. Special attention is paid to the two schemes, i.e. pre-and post- P T symmetric operations. We show that the QFI can be obviously enhanced by means of the P T symmetric operation in different regimes. In addition, we also show that the magnitude of the decoherence involved in the P T symmetric operation can be a general complex number, which extends the applicable scope of the P T symmetric operation approach.
We present an improved phase estimation scheme employing entangled SU(1,1) coherent states in comparison to NOON and entangled coherent states under perfect and lossy conditions for a fixed mean photon number. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized nonlinearity of the phase shifts, both without and with losses. Furthermore, we show that these states give the smallest variance in the phase parameter for a large number of photons in a different order of nonlinearity. Finally, the phase sensitivity of this interferometric setting with parity detection is discussed.