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We study the entanglement between arbitrary two spins in the XY and the antiferromagnetic Heisenberg spin chains in a uniform magnetic field. The entanglement of pairwise qubits in these models is obtained as a function of magnetic field by exact and numerical calculations. We find that the behavior of entanglement in the isotropic XY model is qualitatively the same as that in the Heisenberg model. Properties of entanglement length are also discussed. §1. IntroductionEntanglement is a crucial feature of quantum mechanics directly related to the principle of superposition. The quantum state represented by a nonlocal superposition of two or more quantum systems is called an entangled state. A typical example is the Bell state |ψ = (|01 + |10 )/ √ 2. Many interesting properties of entangled state, such as nonlocality or interference between separate quantum systems, have motivated many researches in the field of quantum information theory.The properties of entanglement have been also investigated recently in the context of the ground state of quantum spin systems. 1)-8) Generally, the ground state of quantum spin systems is highly entangled, and entanglement may play a central roll in quantum collective phenomena, such as quantum phase transition. 9) In this paper we study the behavior of entanglement in quantum spin systems, the XY spin chain and the antiferromagnetic Heisenberg spin chain, adding several new aspects to the existing knowledge. 3), 4) In the next section we briefly review an entanglement measure which quantifies the amount of entanglement of pairwise qubits. Section 3 is devoted to the calculation of entanglement in our spin systems. Summary and discussion are written in §4. §2. Entanglement measure Several measures of entanglement have been proposed. We now use the entanglement of formation 10)-12) which measures the entanglement between pairwise qubits. In the rest of the paper we call simply this measure the entanglement. The entanglement E of a given density matrix ρ of pairwise qubits is defined by

AS bladder tumours, especially papillary tumours, have a low malignancy, they have been treated with such conservative methods as transurethral resection of the tumour, simple resection of the tumour or segmental resection of the bladder wall. Total cystectomy has been carried out in certain cases. Surgeons have considered that total cystectomy may be unnecessarily radical for low-grade papillary tumours.Recently Draper and Stark (1956) and Sanders et a/. (1958) reported animal experiments on mucosal denudation of the bladder, and this method might be a solution to the problem. The present writers have performed this operation clinically with favourable results, which they believe are worth reporting. This submucosal injection of saline solution forms a small wheal. The entire mucosal membrane is then elevated from the muscle layer hy the saline solution. A plane of cleavage is easily developed between the e!evated mucosa and the muscularis.

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