N-particle States Research Articles

Multiparticle extension of the higher spin algebra

Multiparticle extension of a higher spin algebra l is introduced as the Lie superalgebra associated with the universal enveloping algebra U(l). While conventional higher spin symmetry does not mix n-particle states with different n, multiparticle symmetries do so. Quotients of multiparticle algebras are considered, that act on the space of n-particle states with 0 ⩽ n ⩽ k analogous to the space of first k Regge trajectories of string theory. Original higher spin algebra is reproduced at k = 1. Full multiparticle algebras are conjectured to describe vacuum symmetries of string-like extensions of higher spin gauge theories. The relation of the multiparticle algebras with 3D current operator algebras is described. The central charge parameter, to be related to the parameter in AdS/CFT correspondence, enters via the definition of supertrace. Extension to higher p-brane-like symmetries is introduced inductively.

Quantum Sharing an Unknown Multi-Particle State via POVM

Our purpose in this paper is to present a new tripartite quantum state sharing using partially quantum resources. The first scheme is to probabilistically split an unknown n-particle state using pre-shared a partially entangled four-particle cluster state as quantum resource by constructing some proper POVM. This scheme is further extended to share an unknown multi-particle cluster state using different states as quantum resources. Our schemes with general quantum channels are useful for various quantum information processing and quantum network tasks.

Ultra-high energy probes of classicalization

Classicalizing theories are characterized by a rapid growth of the scattering cross section. This growth converts these sort of theories in interesting probes for ultra-high energy experiments even at relatively low luminosity, such as cosmic rays or Plasma Wakefield accelerators. The microscopic reason behind this growth is the production of N-particle states, classicalons, that represent self-sustained lumps of soft Bosons. For spin-2 theories this is the quantum portrait of what in the classical limit are known as black holes. We emphasize the importance of this quantum picture which liberates us from the artifacts of the classical geometric limit and allows to scan a much wider landscape of experimentally-interesting quantum theories. We identify a phenomenologically-viable class of spin-2 theories for which the growth of classicalon production cross section can be as efficient as to compete with QCD cross section already at 100TeV energy, signaling production of quantum black holes with graviton occupation number N ∼ 104.

Cryptanalysis and melioration of secure quantum sealed-bid auction with post-confirmation

We investigate the quantum sealed-bid auction protocol proposed by Zhao et al. (Opt Commun 283:1394, 2010). It uses M groups n-particle GHZ states to represent bids and a post-confirmation mechanism to guarantee the honesty of the quantum sealed-bid auction. However, in our opinion the protocol still does not complete the task of a sealed-bid auction fairly. It is shown that a large group of dishonest bidders can collude to obtain all the other one's secret bids before the opening phase of the auction with a probability polynomially close to one. Moreover, a simple feasible improvement of the protocol is proposed.

Quantum Codes Give Counterexamples to the Unique Preimage Conjecture of theN-Representability Problem

It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are "N-representable" is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle preimage, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.

Evolution of the N-particle state in the BCS model

We obtain an exact scheme describing the dynamics of the N-particle state in the BCS model that is similar to the Gel’fand-Yaglom procedure for finding the transition amplitude of the harmonic oscillator with a time-dependent frequency. We find the many-particle spectrum and the eigenfunctions of the BCS Hamiltonian in the limit as the system volume tends to infinity.

Group averaging for de Sitter free fields in terms of hyperspherical functions

We study the convergence of inner products of free fields over the homogeneous spaces of the de Sitter group and show that the convergence of inner products in the case of N-particle states is defined by the asymptotic behavior of hypergeometric functions. We calculate the inner product for two-particle states on the four-dimensional hyperboloid in detail.

Secure quantum sealed-bid auction with post-confirmation

A new secure quantum auction with post-confirmation is proposed, which is a direct application of the multi-particle super dense coding scheme to the auction problem. In this scheme all bidders use M groups n-particle GHZ states to represent their bids. Different from classical auction protocols and the previous secure quantum sealed-bid auction protocols, in the present scheme, by introducing a post-confirmation mechanism the honesty of the quantum sealed-bid auction is guaranteed, i.e., malicious bidders cannot collude with auctioneers. Also by sharing secret keys with the bidders the auctioneer could insure the anonymity of the bidders.

A criterion for quantum teleportation of an arbitrary N-particle state via a 2N-particle quantum channel

A criterion for he tquantum teleportation of an arbitrary N-particle state via a 2N-particle quantum channel is presented by introducing a term of the “judgment operator". Using the criterion, not only the qualitative judgment of the possibility of successful teleportation can be made but also the quantitative calculation of the probability of successful teleportation can be explicitly given. In addition, a new genuine four-qubit entangled state is proposed, which could not belong to the category of previously known states under stochastic local operations and classical communication.

Overlaps in Pilot Wave Field Theories

Recently doubts have been raised about the ability of pilot wave theories with field ontology to recover the predictions of quantum field theory. In particular, Struyve has questioned that the overlap between wave functionals of macroscopically different states with fixed particle number is really non-significant. With numerical computations and some further plausibility arguments we show that the overlap between n-particle states in field theory decreases almost exponentially with the number of particles and becomes non-significant already for small particle numbers.

Group averaging for de Sitter free fields

Perturbative gravity about global de Sitter space is subject to linearization-stability constraints. Such constraints imply that quantum states of matter fields couple consistently to gravity only if the matter state has vanishing de Sitter charges, i.e. only if the state is invariant under the symmetries of de Sitter space. As noted by Higuchi, the usual Fock spaces for matter fields contain no de Sitter-invariant states except the vacuum, though a new Hilbert space of de Sitter-invariant states can be constructed via so-called group-averaging techniques. We study this construction for free scalar fields of arbitrary positive mass in any dimension, and for linear vector and tensor gauge fields in any dimension. Our main result is to show in each case that group averaging converges for states containing a sufficient number of particles. We consider general N-particle states with smooth wavefunctions, though we obtain somewhat stronger results when the wavefunctions are finite linear combinations of de Sitter harmonics. Along the way we obtain explicit expressions for general boost matrix elements in a familiar basis.

MULTI-SCHEME FOR TELEPORTING AN UNKNOWN N-PARTICLE STATE

By a transformation operator, we find that the transformation operator is not related to the unknown N-particle state. Here, we propose a multi-scheme for the teleportation of an arbitrary and unknown N-particle state by using the method of transformation operator. The proper transformation operator depends on the quantum channel and the measurement basis. The theoretical explanations of some quantum channels are given by transformation operators. Furthermore, we give the analysis for teleporting an arbitrary and unknown N-particle state.

Spin-state transition and spin-polaron physics in cobalt oxide perovskites: ab initio approach based on quantum chemical methods

A fully ab initio scheme based on quantum chemical wavefunction methods is used to investigate the correlated multiorbital electronic structure of a 3d-metal compound, LaCoO3. The strong short-range electron correlations, involving both Co and O orbitals, are treated by multireference techniques. The use of effective parameters such as the Hubbard U and interorbital U′, J terms and the problems associated with their explicit calculation are avoided with this approach. We compute the ordering of the lowest N-particle states in the parent compound and provide new insight into the nature of charge carriers in the hole-doped material. Our results suggest that the transition to a magnetically active state at about 90 K in LaCoO3 involves a high-spin, t2g4eg2 configuration. Additionally, we explain the paramagnetic phase in the low-temperature lightly doped compound through the formation of Zhang–Rice-like oxygen hole states and ferromagnetic clusters.

Secure quantum sealed-bid auction

A new experimentally feasible and secure quantum sealed-bid auction protocol using quantum secure direct communication based on GHZ states is proposed. In this scheme all bidders Bob, Charlie,…, and Zach use M groups n-particle GHZ states to represent their bids. Here, an auctioneer gives the auction outcome by performing a sequence of n-particle GHZ-basis measurements on the final quantum states. It has been shown that using this method guarantees the honesty of the protocol, and malicious bidders can not collude with the auctioneers.

Towards quantum noncommutativeκ-deformed field theory

We introduce a new {kappa}-star product describing the multiplication of quantized {kappa}-deformed free fields. The {kappa} deformation of local free quantum fields originates from two sources: noncommutativity of space-time and the {kappa} deformation of field oscillators algebra; we relate these two deformations. We demonstrate that for a suitable choice of {kappa}-deformed field oscillators algebra, the {kappa}-deformed version of the microcausality condition is satisfied, and it leads to the deformation of the Pauli-Jordan commutation function defined by the {kappa}-deformed mass shell. We show by constructing the {kappa}-deformed Fock space that the use of the {kappa}-deformed oscillator algebra permits one to preserve the bosonic statistics of n-particle states. The proposed star product is extended to the product of n fields, which for n=4 defines the interaction vertex in perturbative description of the noncommutative quantum {lambda}{phi}{sup 4} field theory. It appears that the classical four-momentum conservation law is satisfied at the interaction vertices.

Covariant particle exchange for κ-deformed theories in [formula omitted] dimensions

We consider the exchange of identical scalar particles in theories with κ-deformed Poincaré symmetry. We argue that, at least in 1 + 1 dimensions, the symmetric group S N can be realized on the space of N-particle states in a κ-covariant fashion. For the case of two particles this realization is unique: we show that there is only one non-trivial intertwiner, which automatically squares to the identity.

Quantum Teleportation Schemes of an N-Particle State via Three-Particle General W States

Two schemes of teleporting an N-particle arbitrary and unknown state are proposed when N groups of three-particle general W states are utilized as quantum channels. In the first scheme, the quantum channels are shared by the sender and the recipient. After the sender's Bell-state measurements on his (her) particles, the recipient carries out unitary transformations on his (her) particles. And then, the recipient performs computational basis measurements to realize the teleportation. The recipient can recover the state on either of particle sequences with the equal maximal probability of successful teleportation if he (she) performs appropriate unitary transformations. In the second scheme, the quantum channels are shared by the sender, the recipient and the third ones. After the sender's Bell-state measurements and the third ones' computational basis measurements if they agree to cooperate, the recipient will introduce auxiliary particles and carry out appropriate unitary transformations. Finally, the recipient performs computational basis measurements to fulfill the teleportation. The second scheme can be realized if and only if the third ones agree to cooperate with the recipient.

κ-DEFORMED STATISTICS AND CLASSICAL FOUR-MOMENTUM ADDITION LAW

We consider κ-deformed relativistic symmetries described algebraically by modified Majid–Ruegg bi-cross-product basis and investigate the quantization of field oscillators for the κ-deformed free scalar fields on κ-Minkowski space. By modification of standard multiplication rule, we postulate the κ-deformed algebra of bosonic creation and annihilation operators. Our algebra permits one to define the n-particle states with classical addition law for the four-momentum in a way which is not in contradiction with the nonsymmetric quantum four-momentum co-product. We introduce κ-deformed Fock space generated by our κ-deformed oscillators which satisfy the standard algebraic relations with modified κ-multiplication rule. We show that such a κ-deformed bosonic Fock space is endowed with the conventional bosonic symmetry properties. Finally we discuss the role of κ-deformed algebra of oscillators in field-theoretic noncommutative framework.

Teleportation of arbitrary three-particle GHZ state using single three-particle maximal GHZ state or two EPR states

Two schemes, using respectively the single three-particle maximal Greenberger-Horne-Zeilinger (GHZ) state and the two Einstein-Podolsky-Rosen (EPR) states as quantum channels, for deterministic teleportation of arbitrary three-particle GHZ state are proposed. These schemes are also generalized into the case of teleportation of arbitrary n-particle GHZ state (n≥4). The fidelity of teleportation when the quantum channels are affected by noise is discussed. It is found that when using single three-particle GHZ state which is affected by noise as quantum channel, the fidelity of teleportation is only related to the entanglement of the channel. However, when using two EPR states which is affected by noise as quantum channels, the fidelity of teleportation is related to the entanglement of both the channels and the unknown state to be delivered. Compared with previous proposals, our schemes require a reduced number of entangled states as quantum channels to achieve the same task.

M-BODY PURE STATE ENTANGLEMENT

The simple entanglement of N-body N-particle pure states is extended to the more general M-body or M-body N-particle states where N ≠ M. Some new features of the M-body N-particle pure states are discussed. An application of the measure to quantify quantum correlations in a Bose–Einstien condensate model is demonstrated.