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We consider entanglement in a system of fixed number of identical particles. Since any operation should be symmetrized over all the identical particles and there is the precondition that the spatial wave functions overlap, the meaning of identical-particle entanglement is fundamentally different from that of distinguishable particles. The identical-particle counterpart of the Schmidt basis is shown to be the single-particle basis in which the one-particle reduced density matrix is diagonal. But it does not play a special role in the issue of entanglement, which depends on the single-particle basis chosen. The nonfactorization due to (anti)symmetrization is naturally excluded by using the (anti)symmetrized basis or, equivalently, the particle number representation. The natural degrees of freedom in quantifying the identical-particle entanglement in a chosen single-particle basis are occupation numbers of different single particle basis states. The entanglement between effectively distinguishable spins is shown to be a special case of the occupation-number entanglement. How does one characterize entanglement in a fixed number of identical particles? Obviously, a correct characterization must exclude the nonfactorization due to (anti)symmetrization. Here, we clarify that it can be done by using the (anti)symmetrized basis, which is equivalent to the particle number representation. This naturally leads to the use of occupation numbers of different single-particle basis states as the (distinguishable) degrees of freedom in quantifying identical-particle entanglement even when the number of particles is conserved. The occupation-numbers of different modes have already been used in quantum computing [1]. The use of modes was made in a previous study of identicalparticle entanglement, based on formally mapping the Fock space to the state space of qubits or harmonic oscillators [2], but it was under the unphysical presumption of full access to the Fock space. We shall elaborate that the concept of entanglement in a system of identical particles is fundamentally different from that of distinguishable particles, for which entanglement is invariant under local unitary transformations. There is no local operation that acts only on one of the identical particles. The single-particle basis transformation is made on each particle and chooses a different set of particles in representing the many-particle system. Thus, the entanglement property of a system of identical particles depends on the single-particle basis used. The particle number basis state for a fixed number of particles is just the normalized (anti)symmetrized basis in the configuration space, i.e., Slater determinants or permanents. Therefore, the occupation-number entanglement in a fixed number of particles is nothing but the situation that the state is a superposition of different Slater de- * Email address:ys219@phy.cam.ac.uk terminants or permanents. Another consequence is that the two-identical-particle counterpart of the Schmidt decomposition, which we call Y...

Bacterial chemotaxis is controlled by the signaling of a cluster of receptors. A cooperative model is presented, in which coupling between neighboring receptor dimers enhances the sensitivity with which stimuli can be detected, without diminishing the range of chemoeffector concentration over which chemotaxis can operate. Individual receptor dimers have two stable conformational states: one active, one inactive. Noise gives rise to a distribution between these states, with the probability influenced by ligand binding, and also by the conformational states of adjacent receptor dimers. The two-state model is solved, based on an equivalence with the Ising model in a randomly distributed magnetic field. The model has only two effective parameters, and unifies a number of experimental findings. According to the value of the parameter comparing coupling and noise, the signal can be arbitrarily sensitive to changes in the fraction of receptor dimers to which the ligand is bound. The counteracting effect of a change of methylation level is mapped to an induced field in the Ising model. By returning the activity to the prestimulus level, this adapts the receptor cluster to a new ambient concentration of chemoeffector, and ensures that a sensitive response can be maintained over a wide range of concentrations.

I present some general ideas about quantum entanglement in relativistic quantum field theory, especially entanglement in the physical vacuum. Here, entanglement is defined between different single particle states (or modes), parameterized either by energy-momentum together with internal degrees of freedom, or by spacetime coordinate together with the component index in the case of a vector or spinor field. In this approach, the notion of entanglement between different spacetime points can be established. Some entanglement properties are obtained as constraints from symmetries, e.g., under Lorentz transformation, space inversion, time reverse and charge conjugation.Quantum entanglement is a notion about the structure of a quantum state of a composite system, referring to its non-factorization in terms of states of subsystems. It is regarded as an essential quantum characteristic [1,2]. Entanglement with environment is also crucial in decoherence, i.e. the emergence of classical phenomena in a quantum foundation, and may even be a possible explanation of superselection rules [3,4]. There has been a lot of activities on various aspects of entanglement, including some recent works which take into account relativity [5,6]. Investigations on entanglement in quantum field theories may provide useful perspectives on field theory issues. On the other hand, as the framework of fundamental physics, incorporating relativity, quantum field theory may be useful in deepening our understanding of entanglement. Besides, entanglement due to environmental perturbation may also be helpful in understanding spontaneous symmetry breaking. Most of the methods in field theory adopt Heisenberg or interaction picture, and do not need the explicit form of the underlying quantum state living in an infinite-dimensional Hilbert space. Nevertheless, in many circumstances, it is still important to know the nature of the quantum state, most notably the vacuum. In this paper, as an extension of some previous discussions on non-relativistic quantum field theories [7], I present some general ideas about the nature of entanglement in relativistic quantum field theory, and constraints from symmetries. Such investigations may offer useful insights on the structures of the vacua in quantum field theories on one hand, and on quantum information in relativistic regime on the other hand.First, I describe the basic method here of characterizing entanglement in quantum field theory. In quantum field theory, the dynamical variables are field operators (in real spacetime) or annihilation and creation operators (in energy-momentum space), in terms of which any observable can be expressed. Spacetime coordinate plus the component index in the case of a vector or spinor field, or energy-momentum plus internal degrees of freedoms (such as being particle or antiparticle, spin, polarization, etc.) are merely parameters. These parameters define the modes in either the real spacetime or the momentum space, and exactly provide the labels for the (distinguishable) subsys...

The entanglement between occupation-numbers of different single particle basis states depends on coupling between different single particle basis states in the second-quantized Hamiltonian. Thus in principle, interaction is not necessary for occupation-number entanglement to appear. However, in order to characterize quantum correlation caused by interaction, we use the eigenstates of the singleparticle Hamiltonian as the single particle basis upon which the occupation-number entanglement is defined. Using this so-called proper single particle basis, if there is no interaction, then the manyparticle second-quantized Hamiltonian is diagonalized and thus cannot generate entanglement, while its eigenstates can always be chosen to be non-entangled. If there is interaction, entanglement in the proper single particle basis arises in energy eigenstates and can be dynamically generated. Using the proper single particle basis, we discuss occupation-number entanglement in important eigenstates, especially ground states, of systems of many identical particles, in exploring insights the notion of entanglement sheds on many-particle physics. The discussions on Fermi systems start with Fermi gas, Hatree-Fock approximation, and the electron-hole entanglement in excitations. In the ground state of a Fermi liquid, in terms of the Landau quasiparticles, entanglement becomes negligible. The entanglement in a quantum Hall state is quantified as −f ln f − (1 − f ) ln(1 − f ), where f is the proper fractional part of the filling factor. For BCS superconductivity, the entanglement is a function of the relative momentum wavefunction of the Cooper pair g k , and is thus directly related to the superconducting energy gap, and vanishes if and only if superconductivity vanishes. For a spinless Bose system, entanglement does not appear in the Hatree-Gross-Pitaevskii approximation, but becomes important in the Bogoliubov theory, as a characterization of two-particle correlation caused by the weak interaction. In these examples, the interaction-induced entanglement as calculated is directly related to the macroscopic physical properties.

The body-centered-cubic (bcc) phase of Ni, which does not exist in nature, has been achieved as a thin film on GaAs(001) at 170 K via molecular beam epitaxy. The bcc Ni is ferromagnetic with a Curie temperature of 456 K and possesses a magnetic moment of 0.52+/-0.08 micro(B)/atom. The cubic magnetocrystalline anisotropy of bcc Ni is determined to be +4.0x10(5) ergs x cm(-3), as opposed to -5.7x10(4) ergs x cm(-3) for the naturally occurring face-centered-cubic (fcc) Ni. This sharp contrast in the magnetic anisotropy is attributed to the different electronic band structures between bcc Ni and fcc Ni, which are determined using angle-resolved photoemission with synchrotron radiation.

We report on measurements of the 1S, 2S and 3S di erential cross sections d 2 =dp T dy jyj 0:4 , as well as on the 1S polarization in pp collisions at p s = 1:8TeV using a sample of 77 3 pb ,1 collected by the Collider Detector at Fermilab.The three resonances were reconstructed through the decay ! + , . The measured angular distribution of the muons in the 1S rest frame is consistent with unpolarized meson production.

According to Deutsch, a universal quantum Turing machine (UQTM) is able to perform, in repeating a fixed unitary transformation on the total system, an arbitrary unitary transformation on an arbitrary data state, by including a program as another part of the input state. We note that if such a UQTM really exists, with the program state dependent on the data state, and if the prescribed halting scheme is indeed valid, then there would be no entanglement between the halt qubit and other qubits, as pointed out by Myers. If, however, the program is required to be independent of the data, the concerned entanglement appears, and is problematic no matter whether the halt qubit is monitored or not. We also note that for a deterministic programmable quantum gate array, as discussed by Nielson and Chuang, if the program is allowed to depend on the data state, then its existence has not been ruled out. On the other hand, if UQTM exists, it can be simulated by repeating the operation of a fixed gate array. However, more importantly, we observe that it is actually still open whether Deutsch's UQTM exists and whether a crucial concatenation scheme, of which the halting scheme is a special case, is valid.