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arXiv:2011.09787

An investigation on the nonclassical and quantum phase properties of a family of engineered quantum states

Priya Malpani

Published Nov 19, 2020• 0 citations
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Abstract

The main focus of this thesis is to study the nonclassical and phase properties of a family of engineered quantum states, most of which show various nonclassical features. The beauty of these states is that these states can be used to establish quantum supremacy. Earlier, a considerable amount of works has been reported on various types of quantum states and their nonclassical properties. Here, complementing the earlier works, the effect of non-Gaussianity inducing operators on the nonclassical and phase properties of displaced Fock states have been studied. This thesis includes 6 chapters. In Chapter 1, motivation behind performing the present work is stated explicitly, also the basic concepts of quantum optics are discussed with a specific attention on the witnesses and measures of nonclassicality. In Chapter 2, nonclassical properties of photon added and subtracted displaced Fock states have been studied using various witnesses of lower- and higher-order nonclassicality which are introduced in Chapter 1. In Chapter 3, we have continued our investigation on photon added and subtracted displaced Fock states (and their limiting cases). In this chapter, quantum phase properties of these states are investigated from a number of perspectives, and it is shown that the quantum phase properties are dependent on the quantum state engineering operations performed. In Chapter 4, we have continued our investigation on the impact of non-Gaussianity inducing operators on the nonclassical and phase properties of the displaced Fock states. In Chapter 5, we have performed a comparison between to process that are used in quantum state engineering to induce nonclassical features. Finally, this thesis is concluded in Chapter 6, where we have summarized the findings of this thesis and have also described scope of the future works.

DOI
10.48550/arxiv.2011.09787

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•Oct 24, 2011•0 citations
The main focus of this thesis is to study the nonclassical and phase properties of a family of engineered quantum states, most of which show various nonclassical features. The beauty of these states is that these states can be used to establish quantum supremacy. Earlier, a considerable amount of works has been reported on various types of quantum states and their nonclassical properties. Here, complementing the earlier works, the effect of non-Gaussianity inducing operators on the nonclassical and phase properties of displaced Fock states have been studied. This thesis includes 6 chapters. In Chapter 1, motivation behind performing the present work is stated explicitly, also the basic concepts of quantum optics are discussed with a specific attention on the witnesses and measures of nonclassicality. In Chapter 2, nonclassical properties of photon added and subtracted displaced Fock states have been studied using various witnesses of lower- and higher-order nonclassicality which are introduced in Chapter 1. In Chapter 3, we have continued our investigation on photon added and subtracted displaced Fock states (and their limiting cases). In this chapter, quantum phase properties of these states are investigated from a number of perspectives, and it is shown that the quantum phase properties are dependent on the quantum state engineering operations performed. In Chapter 4, we have continued our investigation on the impact of non-Gaussianity inducing operators on the nonclassical and phase properties of the displaced Fock states. In Chapter 5, we have performed a comparison between to process that are used in quantum state engineering to induce nonclassical features. Finally, this thesis is concluded in Chapter 6, where we have summarized the findings of this thesis and have also described scope of the future works.
Abstract Quantum phase properties of photon added and subtracted displaced Fock states (and their limiting cases) are investigated from a number of perspectives, and it is shown that the quantum phase properties are dependent on the quantum state engineering operations performed. Specifically, the analytic expressions for quantum phase distributions and angular Q distribution as well as measures of quantum phase fluctuation and phase dispersion are obtained. The uniform phase distribution of the initial Fock states is observed to be transformed by the unitary operation (i.e., displacement operator) into non‐Gaussian shape, except for the initial vacuum state. It is observed that the phase distribution is symmetric with respect to the phase of the displacement parameter and becomes progressively narrower as its amplitude increases. The non‐unitary (photon addition/subtraction) operations make it even narrower in contrast to the Fock parameter, which leads to broadness. The photon subtraction is observed to be a more powerful quantum state engineering tool in comparison to the photon addition. Further, one of the quantum phase fluctuation parameters is found to reveal the existence of antibunching in both the engineered quantum states under consideration. Finally, the relevance of the engineered quantum states in the quantum phase estimation is also discussed.
Non-Gaussian and nonclassical states and processes are already found to be important resources for performing various tasks related to quantum gravity and quantum information processing. The effect of non-Gaussianity inducing operators on the nonclassicality of quantum states has also been studied rigorously. Considering these facts, a quantitative analysis of the nonclassical and non-Gaussian features is performed here for photon added displaced Fock state, as a test case, using a set of measures like entanglement potential, Wigner Yanese skew information, Wigner logarithmic negativity and relative entropy of non-Gaussianity. It is observed that photon addition (Fock parameter) significantly increases the amount of nonclassicalty and non-Gaussianity for small (large) values of the displacement parameter, which decreases both the quantum features monotonically. In this respect, the role of Fock parameter is found to be more prominent and stronger compared to photon addition. Finally, the dynamics of Wigner function under the effect of photon loss channel is used to show that only highly efficient detectors are able to detect Wigner negativity.
Abstract Nonclassical properties of photon added and subtracted displaced Fock states are studied using various witnesses of lower‐ and higher‐order nonclassicality. Compact analytic expressions are obtained for the nonclassicality witnesses. Using those expressions, it is established that these states and the states that can be obtained as their limiting cases (except coherent states) are highly nonclassical as they show the existence of lower‐ and higher‐order antibunching and sub‐Poissonian photon statistics, in addition to the nonclassical features revealed through the Mandel parameter, zeros of Q function, Klyshko's criterion, and Agarwal–Tara criterion. Further, some comparison between the nonclassicality of photon added and subtracted displaced Fock states have been performed using witnesses of nonclassicality. This has established that between the two types of non‐Gaussianity inducing operations (i.e., photon addition and subtraction) used here, photon addition influences the nonclassical properties more strongly. Further, optical designs for the generation of photon added and subtracted displaced Fock states from squeezed vacuum state have also been proposed.
This thesis fathoms the possibilities and limitations of measurements in quantum optics. After a short introduction to the general aspects of measurements in quantum mechanics, it presents three examples of a measurement process in concrete applications to quantum optics. For one, while operators describing quantities of interest might have a simple theoretical form, it is often hard to actually implement a measurement of their expectation values experimentally. This situation is encountered in the first part which is devoted to the measurement of quantum statistical properties of a light beam. In contrast to classical optics, these statistics are not fully determined by first- and second-order correlations. Instead, higher-order correlations, usually described by non-Hermitian operators, are necessary to characterize the quantum state completely. A particular example is the N-photon Fock state, for which only a measurement of the Nth-order correlations allows for a full characterization. Here, we present a new method how to measure an important class of Nth-order correlations for arbitrary N in a single spatial mode with two polarizations with limited experimental resources. The second part is again centered around the realization of specific measurement operators for photon correlation measurements. However, in contrast to the previous chapter, these measurements are not an end in their own, but are designed to create specific quantum states as a consequence of the measurement process: A suitable measurement of photons emitted by a number of atoms allows to transfer the atoms into long-lived entangled states. We find that with this method it is possible to entangle two remote atomic qubits to an arbitrary and well-defined degree. Furthermore, we show how to generate two families of quantum states in an arbitrary number of remote atomic qubits: one family consists of all -- symmetric and non-symmetric -- total angular momentum eigenstates in N remote qubits, the other is a family of cluster states. It is also systematically investigated whether the technique of quantum state engineering by projective measurements allows for the creation of any arbitrary state. We find explicit solutions for the case of two and three qubits, while it is shown that no solution exist for N > 6. We conclude the section by proving that with some changes in the setup, this measurement-based quantum state engineering technique allows to create the same states among the scattered photons themselves rather than among the emitting atoms. The last part is devoted to the amount of information one is able to gain about a given system when performing a measurement. The corresponding limits of information are investigated at the example of the duality that arises in a two-way interferometer between the visibility of the interference pattern and the knowledge about the path of the interfering object. We show that there exist correlations between the phase difference the interfering object acquires on its way through the interferometer and the amount of which-way information retrievable from certain observables of the which-way detector. In this way, the which-way information becomes a phase-dependent quantity. In particular, we find that for certain values of the phase shift, the amount of extractable which-way information can be larger than allowed by phase-independent measurement. This property is put to use to find the optimal observable for the which-way detector readout in dependence on the phase of the interfering object. Following this strategy, we are able to gain more which-way information than previously thought possible.