Entanglement sharing and decoherence in the spin-bath

Abstract

The monogamous nature of entanglement has been illustrated by the derivation of entanglement-sharing inequalities-bounds on the amount of entanglement that can be shared among the various parts of a multipartite system. Motivated by recent studies of decoherence, we demonstrate an interesting manifestation of this phenomena that arises in system-environment models where there exists interactions between the modes or subsystems of the environment. We investigate this phenomenon in the spin-bath environment, constructing an entanglement-sharing inequality bounding the entanglement between a central spin and the environment in terms of the pairwise entanglement between individual bath spins. The relation of this result to decoherence will be illustrated using simplified system-bath models of decoherence. While entanglement is argued to be the distinguishing feature of quantum computers, responsible for their power ͓1͔, it is also the source of one of the major obstacles in their construction. Decoherence, the process by which a quantum superposition state decays into a classical, statistical mixture of states, is caused by entangling interactions between the system and its environment ͓2͔. Somewhat paradoxically, the quantum entanglement between a system and its environment induces classicality in the system. While it is still a contentious topic as to whether quantum computation will be possible in the face of decoherence, Zurek ͓3͔ has demonstrated that decoherence is necessary to facilitate the measurement of a quantum system. Understanding decoherence lies at the heart of measurement, quantum information processing, and, more fundamentally, the transition from the quantum to the classical world.The road to studying decoherence by explicitly modeling system-environment interactions has led to simple models of the quantum environment. Environments can be modeled as either baths of harmonic oscillators ͓4͔ or spins ͑with spin 1 2 ͒ argued to represent distinct types of environmental modes ͓5͔. The simplest system-environment models consist of a central spin ͑or qubit͒ coupled to the environment-i.e., the spin-boson model ͓4͔-which has applications to the decoherence of qubits for quantum information processing.Decoherence of a spin-1 2 particle at low temperatures may be conveniently modeled by the "central spin" model, which couples a central spin- where H S and H B are the internal Hamiltonians of the central spin and spin bath, respectively, and H SB is the coupling term. Denote the state of the system-environment at time t by SB ͑t͒. Initially at t = 0 we take the central spin S to be in a pure state, uncorrelated with the bath. That is,for some initial state of the bath B ͑0͒. Typically B ͑0͒ is taken to be a thermal state of the Hamiltonian H B or, at low temperatures, the ground state. As the system evolves under H the central spin becomes coupled to the bath, and its reduced density matrix S ͑t͒ at later times is no longer pure. The central spin is said to have decohered, and the amount of decoherence is t...

Controllable dynamics of two separate qubits in Bell states

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“…Recent work suggests that the internal dynamics of the environment can be crucial to the decoherence of the central system. [3][4][5][6][7][8][9][10][11][12][13][14][15] In this paper, we present results of extensive simulation work of a two-spin system interacting with a spin-bath environment and show that the decoherence of the two-spin system can exhibit different behaviors, depending on the characteristics of the coupling with the environment, the internal dynamics, and the initial state of the latter. We also provide a simple physical picture to understand this behavior.…”

Rabi oscillations, decoherence, and disentanglement in a qubit–spin-bath system

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