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arXiv:quant-ph/0204054 · Physical Review A

Degree of entanglement in a quantum-measurement process

Matthias Jakob, Yonatan Abranyos, János A. Bergou

Published Aug 27, 2002• 11 citations
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Abstract

We suggest a quantum-measurement model in an ion trap that specifies the probability distribution of two distinct internal ground states of a trapped four-level ion. The external degrees of motion of the four-level ion constitute the meter that, in turn, is coupled to the environment by engineered reservoirs. In a previous publication, a similar measurement model was employed to test decoherence effects on quantum nonlocality in phase space on the basis of coincidence measurements of the entangled system-meter scheme. Here, we study the effects of decoherence on the entanglement of formation characterized by the concurrence. The concurrence of the system enables us to find the maximum possible violation of the Bell inequality. Surprisingly, this model gives illustrative insights into the question as to what extent the Bell inequality can be considered as a measure of entanglement.

DOI
10.1103/physreva.66.022113

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Journal of Modern Optics•Jun 15, 2001•17 citations
We suggest a quantum-measurement model in an ion trap that specifies the probability distribution of two distinct internal ground states of a trapped four-level ion. The external degrees of motion of the four-level ion constitute the meter that, in turn, is coupled to the environment by engineered reservoirs. In a previous publication, a similar measurement model was employed to test decoherence effects on quantum nonlocality in phase space on the basis of coincidence measurements of the entangled system-meter scheme. Here, we study the effects of decoherence on the entanglement of formation characterized by the concurrence. The concurrence of the system enables us to find the maximum possible violation of the Bell inequality. Surprisingly, this model gives illustrative insights into the question as to what extent the Bell inequality can be considered as a measure of entanglement.
We propose a quantum measurement model where the environment is taken to be a squeezed reservoir. This kind of meter-environment coupling has a dramatic influence on the decoherence rate. Depending on the phase and the squeezing parameter the decoherence time can be enhanced or reduced arbitrarily. We derive the Wigner function for the system-meter state, and discuss its nonclassical features. Further, we test quantum nonlocality in phase space on the basis of coincidence measurements of the entangled system-meter scheme, and investigate the effect of a highly reduced decoherence rate. Surprisingly, in sharp contrast to popular notion, violations of the Bell inequality can be observed even when the meter has reached a macroscopic state.
We propose an alternative evaluation of quantum entanglement by measuring the maximum violation of the Bell’s inequality without information of the reduced density matrix of a system. This proposal is demonstrated by bridging the maximum violation of the Bell’s inequality and a concurrence of a pure state in an n-qubit system, in which one subsystem only contains one qubit and the state is a linear combination of two product states. We apply this relation to the ground states of four qubits in the Wen-Plaquette model and show that they are maximally entangled. A topological entanglement entropy of the Wen-Plaquette model could be obtained by relating the upper bound of the maximum violation of the Bell’s inequality to the generalized concurrence of a pure state with respect to different bipartitions.
In this study, our goal is to obtain the entanglement dynamics of trapped three-level ion interaction two laser beams in beyond Lamb-Dicke parameters. Three values of LDP, η=0.09, η=0.2 and η=0.3 are given. We used the concurrence and the negativity to measure the amount of quantum entanglement created in the system. The interacting trapped ion led to the formation of phonons as a result of the coupling. In two quantum systems (ion-phonons), analytical formulas describing both these measurements are constructed. These formulas and probability coefficients include first order terms of final state vector. We report that long survival time of entanglement can be provided with two quantum measures. Negativity and concurrence maximum values are obtained N = 0.553 and for LDP = 0.3. As a similar, the other two values of LDP are determined and taken into account throughout this paper. For a more detailed understanding of entanglement measurement results, “contour plot” was preferred in Mathematica 8.
Quantum systems are inherently open and fragile, leading to the loss of information and quantum properties to the environment. This study investigates the behavior of quantum entanglement (QE), quantum nonlocality (QN), and measurement uncertainty in a two-atom system interacting with a common dissipative thermal reservoir under the Markovian approximation. QE is measured using concurrence, QN through the CHSH-Bell inequality, and uncertainty through the quantum memory-assisted entropic uncertainty relation (QMA-EUR). The findings show that both QE and QN decay as the scaled time and excitation numbers increase, with QE being more resilient. In contrast, QMA-EUR shows an anticorrelation with concurrence and CHSH-Bell violation, increasing as these properties diminish. Adjusting the system initial-state parameters improves QE and CHSH degree of violation, while reducing uncertainty. Over long durations, concurrence and CHSH-Bell violations disappear, while QMA-EUR stabilizes at its maximum value. These results highlight the importance of precise parameter control to enhance quantum features and predict outcomes, especially for bipartite systems initialized in a Werner-like state.
Abstract Nonlocality, manifested by the violation of Bell inequalities, indicates entanglement within a joint quantum system. A natural question is how much entanglement is required for a given nonlocal behavior. Here, we explore this question by quantifying entanglement using a family of generalized Clauser–Horne–Shimony–Holt-type Bell inequalities. Given a Bell-inequality violation, we derive analytical lower bounds on the entanglement of formation, a measure related to entanglement dilution. The bounds also lead to an analytical estimation of the negativity of entanglement. In addition, we consider one-way distillable entanglement tied to entanglement distillation and derive tight numerical estimates. With the additional assumptions of qubit-qubit systems, we find that the relationship between entanglement and measurement incompatibility is not simply a trade-off under a fixed nonlocal behavior. Furthermore, we apply our results to two realistic scenarios—non-maximally entangled and Werner states. We show that one can utilize the nonlocal statistics by optimizing the Bell inequality for better entanglement estimation.
Abstract. Entanglement is a critical resource used in many current quantum information schemes. As such entanglement has been extensively studied in two qubit systems and its entanglement nature has been exhibited by violations of the Bell inequality. Can the amount of violation of the Bell inequality be used to quantify the degree of entanglement? What do Bell inequalities indicate about the nature of entanglement? Entanglement was recognized early as one of the key features of quantum mechanics [1, 2]. Entanglement can be described as the correlation between distinct subsystems which cannot be created by local actions on each subsystem separately. The advantage o ered by quantum entanglement relies on the crucial premise that it cannot be reproduced by any classical theory [3-5]. Despite the fact that the possibility of quantum entanglement was acknowledged almost as soon as quantum theory was discovered, it is only in recent years that consideration has been given to nding methods to quantify it [6-17]. Historically the Bell inequal-ities were seen as a means of determining whether a two qubit system is entangled.