Entangled Systems

Bipin R. Desai

Ngo Phuc Duc Loc

If time is emergent, quantum system is entangled with quantum time as it evolves. If the system contains entanglement within itself, which we can call internal entanglement to distinguish it from the "external" time-system entanglement, the speed of evolution is enhanced. In this paper, we show the correlation between the novel time-system entanglement and the conventional internal entanglement of a system that contains two entangled qubits. We consider two cases: (1) two initially entangled qubits that evolve under local dynamics; (2) two interacting qubits such that entanglement between them is generated over time. In the first case, we obtain the main result that increasing internal entanglement speeds up the evolution and makes the system more entangled with time. For both cases, we show the dependence of time-system entanglement entropy on the distance of evolution which is characterized by fidelity. The interacting system can evolve faster than the non-interacting system if the interaction is sufficiently strong, and thus it can be entangled with time more efficiently.

Tomasz Bigaj

In their 2002 article, Ghirardi, Marinatto and Weber have proposed a formal analysis of the entanglement properties for a system consisting of N distinguishable particles. Their analysis leads to the differentiation of three possible situations that can arise in such systems: complete entanglement, complete non-entanglement, and the remaining cases. I argue that this categorization leaves out one important possibility in which a system is completely entangled, and yet some of its subsystems are mutually non-entangled. As an example I present and discuss a state of a three-particle system which cannot be decomposed into two non-entangled systems, and yet particle number one is not entangled with particle number three. Consequently, I introduce a new notion of utter entanglement, and I argue that some systems may be completely but not utterly entangled.

Sergei Kurgalin, Sergei Borzunov

Xiaodong Zhang, Ya-Fei Yu, Zhi‐Ming Zhang

An appropriate weak value can be used to amplify weak physical parameters and improve the precision of parameter estimation in the process of quantum weak measurement. The increase of the precision of such a parameter estimation may originate from the entanglement in the system. This paper uses Fisher information to study the influence of the entanglement in the system and the entanglement between the system and the pointer on the estimation precision of the coupling parameters between the system and the pointer in the process of weak measurement. The entanglement of the entangled pure state of the GHZ-like state and the entangled mixed state affected by the depolarization noise and the influence of the entanglement between the system and the pointer on the parameter estimation are analyzed. The results show that the Fisher information quantity increases with the increase of the initial state entanglement degree of the system when the initial state of the system is an entangled pure state or an entangled mixed state affected by depolarization noise, and both the Fisher information quantity and the post-selection probability reach their maximum values when the initial and final state of the system are both the maximum entangled states; but the weaker the entanglement between the system and the pointer, the more the Fisher information obtained in the measurement will be and the higher the accuracy of parameter estimation. These research results show that the entanglement in the system will improve the precision of parameter estimation, while the entanglement between the system and the pointer will reduce the precision of parameter estimation.

Mario S. Reis