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Journal of Modern Optics

Analyzing dissipation effects on the non-classicality witnessing by a qubit via the entangled state representation

E. Nahvifard

Published Mar 17, 2020• 1 citation
Publisher

Abstract

In this paper, we study detection of the state non-classicality for a quantum harmonic oscillator by a qubit in the presence of dissipation effects. We show that dissipation can enhance the effectiveness of the method in case of using the corrected form of the related nonclassicality witness. Such an improvement is attributed to the fact that dissipation leads to probing a surface, instead of a curve, of the complex plane for non-classicality condition on normally-ordered characteristic function.

DOI
10.1080/09500340.2020.1741712

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Acta Physica Sinica•Jan 1, 2024•0 citations
In this paper, we study detection of the state non-classicality for a quantum harmonic oscillator by a qubit in the presence of dissipation effects. We show that dissipation can enhance the effectiveness of the method in case of using the corrected form of the related nonclassicality witness. Such an improvement is attributed to the fact that dissipation leads to probing a surface, instead of a curve, of the complex plane for non-classicality condition on normally-ordered characteristic function.
A dynamics-based test, originally proposed by Tsirelson for the harmonic oscillator, provides a method for certifying quantumness under the assumption of a known Hamiltonian. These tests, however, are typically proposed for isolated systems, an assumption that breaks down in experimental implementation. In this paper, we extend the protocol to the harmonic oscillator coupled to standard models of dissipation: thermal relaxation, pure dephasing, and the Caldeira--Leggett model. Using the Moyal-Wigner formalism of quantum mechanics in phase space, we show that the introduction of dissipation requires a dissipation-dependent shift of the classical bound, and provide the threshold under which the nonclassicality witness retains its validity.
We introduce a family of entanglement witnesses for continuous variable systems, which rely on the sole assumption that their dynamics is that of coupled harmonic oscillators at the time of the test. Entanglement is inferred from the Tsirelson nonclassicality test on one of the normal modes, without any knowledge about the state of the other mode. In each round, the protocol requires measuring only the sign of one coordinate (e.g., position) at one among several times. This dynamic-based entanglement witness is more akin to a Bell inequality than to an uncertainty relation: in particular, it does not admit false positives from classical theory. Our criterion detects non-Gaussian states, some of which are missed by other criteria.
Based on the entropic uncertainty relation in the presence of quantum memory, the entanglement witness of two atoms in dissipative cavities is investigated by using the time-convolutionless master-equation approach. We discuss in detail the influences of the non-Markovian effect and the atom–cavity coupling on the lower bound of the entropic uncertainty relation and entanglement witness. The results show that, with the coupling increasing, the number of the time zone witnessed will increase so that the entanglement can be repeatedly witnessed. Enhancing the non-Markovian effect can add the number of the time zone witnessed and lengthen the time of entanglement witness. The results can be applied in quantum measurement, entanglement detecting, quantum cryptography task, and quantum information processing.
We study nonclassical effects in the dynamics of an open quantum system. The model involves a harmonic oscillator coupled to a reservoir of non-interacting harmonic oscillators. Different system-bath interaction schemes as well as reservoir states are considered. Particularly, the squeezed reservoirs coupled to the system through single and two quanta exchange processes are put in the spotlight. We investigate the quantumness conveyed to the system through the bath by computing a nonclassicality measure for different bath properties and when the memory effects are appreciable. The measure of nonclassicality is calculated for projective measurements both in the number state basis and a basis formed by a set of coherent states. Our results show that in both bases the measure exhibits characteristic features for each bath state and the form of its interaction with the system. Some of those features are independent from the measurement scheme (number or coherent), and thus, emergent from the bath and its interaction with the probe system. This allows for fingerprinting and identifying the environmental effects by tracking a given probe with appropriate measurements. Hence, may prove useful for distinguishing different sources of decoherence.
The quantum oscillator model plays a significant role in quantum optics and quantum information and has been one of the hot topics in related research fields. Inspired by the single-mode linear harmonic oscillator and the two-mode entangled state representation, we construct a two-mode coupled harmonic oscillator in this work. Different from the quantum transformation method used in previous literature, the entangled state representation is directly used in this work to solve its energy eigenvalues and eigenfunctions easily. The energy eigenvalues and eigenfunctions of this two-mode coupled harmonic oscillator are continuous compared with those of the one-mode harmonic oscillator. Using the matrix theory of quantum operators, we derive the transformation and inverse transformation of the time evolution operator corresponding to the two-mode coupled harmonic oscillator. In addition, using the entangled state representation, the specific form of the time evolution of the two-mode vacuum state under the action of the oscillator is obtained. Through the analysis of quantum fidelity, it is found that the fidelity of the output quantum state decreases with the oscillator frequency increasing, and the fidelity eventually tends to zero with the increase of time. When analyzing the orthogonal squeezing properties of the output quantum state, this type of two-mode oscillator does not have the orthogonal squeezing effect, but it has a strong quantum dissipation effect instead. This conclusion is further verified by the quasi-probability distribution Q function of the quantum state phase space. Therefore, the two-mode coupled harmonic oscillator has a major reference value in quantum control such as quantum decoherence and quantum information transmission. Like the two-mode squeezed vacuum state, the photon distribution of the output quantum light field corresponding to the two-mode harmonic oscillator presents a super-Poisson distribution, and the photons exhibit a strong anti-bunching effect. Using the three-dimensional discrete plot of the photon number distribution, the super-Poisson distribution and quantum dissipation effect of the output quantum state are intuitively demonstrated. Finally, the SV, which is an entanglement criterion, is used to determine that the output quantum state has a high degree of entanglement. Further numerical analysis shows that the degree of entanglement increases with the action time and the oscillator frequency. In summary, the two-mode coupled harmonic oscillator constructed in this work can be used to prepare highly entangled quantum states through a complete quantum dissipation process. This provides theoretical support for experimental preparing quantum entangled states based on dissipative mechanisms.