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arXiv:quant-ph/0703083 · Journal of Modern Optics

Negative entanglement measure, and what it implies

Ting Yu, Joseph H. Eberly

Published Sep 10, 2007• 24 citations
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Abstract

In this paper, we extract from concurrence its variable part, denoted Λ, a function of density matrix ρ, either positive or negative. We use it to investigate entanglement dynamics of two isolated but initially entangled qubits, each coupled to its own environment. In particular, we show that it can signal whether the disentanglement of an entangled state occurs in a finite time.

DOI
10.1080/09500340701432581

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The European Physical Journal Special Topics•Feb 20, 2019•1 citation
In this paper, we extract from concurrence its variable part, denoted Λ, a function of density matrix ρ, either positive or negative. We use it to investigate entanglement dynamics of two isolated but initially entangled qubits, each coupled to its own environment. In particular, we show that it can signal whether the disentanglement of an entangled state occurs in a finite time.
In this paper, we extract from concurrence its variable part, denoted Lambda\\LambdaLambda, and use Lambda\\LambdaLambda as a time-dependent measure of "distance", either postive or negative, from the separability boundary. We use it to investigate entanglement dynamics of two isolated but initially entangled qubits, each coupled to its own environment.
We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso- and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then work out an analog of the Born–Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement (Entanglement Sudden Death) at finite moments and its revivals (Entanglement Sudden Birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.
We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment.We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso-and even nanosize.We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition.We then workout an analog of Born-Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord.We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits.In particular, we find the vanishing of the entanglement at finite moments and its subsequent revivals (entanglement sudden death and entanglement sudden birth).Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.
We study the entanglement dynamics of multi-qubit systems coupled to a common dissipative environment, focusing on systems with one or two initially excited qubits. Using the Lindblad master equation, we derive the time evolution of the density matrix and analyze the entanglement between qubit pairs via the concurrence measure. The solution method involves applying the Lindblad super-operator to the initial density matrix, generating a subspace of non-duplicate states. We extend our analysis to nnn-qubit systems, including three-qubit and four-qubit configurations, and explore the effects of thermal noise on entanglement dynamics. Our results demonstrate how initial conditions, system size, and environmental interactions shape entanglement, providing valuable insights for quantum information processing applications.