In this paper, we consider teleportation capability, distillability, and nonlocality on three-qubit states. In order to investigate some relations among them, we first find the explicit formulas of the quantities about the maximal teleportation fidelity on three-qubit states. We show that if any three-qubit state is useful for three-qubit teleportation then the three-qubit state is distillable into a Greenberger-Horne-Zeilinger state, and that if any three-qubit state violates a specific form of Mermin inequality then the three-qubit state is useful for three-qubit teleportation.In this paper, we consider teleportation capability, distillability, and nonlocality on three-qubit states. In order to investigate some relations among them, we first find the explicit formulas of the quantities about the maximal teleportation fidelity on three-qubit states. We show that if any three-qubit state is useful for three-qubit teleportation then the three-qubit state is distillable into a Greenberger-Horne-Zeilinger state, and that if any three-qubit state violates a specific form of Mermin inequality then the three-qubit state is useful for three-qubit teleportation.

arXiv:quant-ph/0702247Physical Review AJul 13, 200727 citations

Violation of Mermin–Ardehali–Belinksii–Klyshko inequality in the three-Jaynes–Cummings model

LU Dao-ming

In this paper, we consider the situation that three identical two-level atoms are separately trapped in the three single-mode cavities. Each atom resonantly interacts with cavity via a one-photon hopping. The dynamics of nonlocality in the system is investigated via Mermin–Ardehali–Belinksii–Klyshko inequality. The results show that when three atoms are initially in W state and three-cavity fields are in vacuum states both the quantum state of three atoms and that of three cavities all display nonlocality On the other hand, when three atoms are initially in Greenberger–Horne–Zeilinger state and three-cavity fields are in vacuum states, the quantum state of three atoms and that of three cavities all do not display nonlocality.In this paper, we consider the situation that three identical two-level atoms are separately trapped in the three single-mode cavities. Each atom resonantly interacts with cavity via a one-photon hopping. The dynamics of nonlocality in the system is investigated via Mermin–Ardehali–Belinksii–Klyshko inequality. The results show that when three atoms are initially in W state and three-cavity fields are in vacuum states both the quantum state of three atoms and that of three cavities all display nonlocality On the other hand, when three atoms are initially in Greenberger–Horne–Zeilinger state and three-cavity fields are in vacuum states, the quantum state of three atoms and that of three cavities all do not display nonlocality.

Journal of Modern OpticsOct 25, 20184 citations

And Then There Was One

Anonymous

PhysicsFeb 9, 20120 citations

There can be only one

Matthias Weidemüller

Nature PhysicsFeb 1, 200924 citations

Three-body scattering hypervolume of two-component fermions in three dimensions

Jiansen Zhang, Zipeng Wang, Shina Tan

We study the zero-energy collision of three fermions, two of which are in the spin-down ($\ensuremath{\downarrow}$) state and one of which is in the spin-up ($\ensuremath{\uparrow}$) state. Assuming that the two-body and three-body interactions have a finite range, we find a parameter $D$ called the three-body scattering hypervolume. We study the three-body wave function asymptotically when three fermions are far apart or one spin-$\ensuremath{\uparrow}$ (spin-$\ensuremath{\downarrow}$) fermion and one pair, formed by the other two fermions, are far apart and derive three asymptotic expansions of the wave function. The three-body scattering hypervolume $D$ appears in the coefficients of such expansions at the order of ${B}^{\ensuremath{-}5}$, where $B={[({s}_{1}^{2}+{s}_{2}^{2}+{s}_{3}^{2})/2]}^{1/2}$ is the hyperradius of the triangle formed by the three fermions (we assume that the three fermions have the same mass), and ${s}_{1}, {s}_{2}, {s}_{3}$ are the sides of the triangle. We compute the $T$ -matrix element for three such fermions colliding at low energy in terms of $D$ in the absence of two-body interactions. When the interactions are weak, we calculate $D$ approximately using the Born expansion. We also analyze the energy shift of three two-component fermions in a large periodic cube due to $D$ and generalize this result to the many-fermion system. $D$ also determines the three-body recombination rates in two-component Fermi gases, and we calculate the three-body recombination rates in terms of $D$ and the density and temperature of the gas.We study the zero-energy collision of three fermions, two of which are in the spin-down ($\ensuremath{\downarrow}$) state and one of which is in the spin-up ($\ensuremath{\uparrow}$) state. Assuming that the two-body and three-body interactions have a finite range, we find a parameter $D$ called the three-body scattering hypervolume. We study the three-body wave function asymptotically when three fermions are far apart or one spin-$\ensuremath{\uparrow}$ (spin-$\ensuremath{\downarrow}$) fermion and one pair, formed by the other two fermions, are far apart and derive three asymptotic expansions of the wave function. The three-body scattering hypervolume $D$ appears in the coefficients of such expansions at the order of ${B}^{\ensuremath{-}5}$, where $B={[({s}_{1}^{2}+{s}_{2}^{2}+{s}_{3}^{2})/2]}^{1/2}$ is the hyperradius of the triangle formed by the three fermions (we assume that the three fermions have the same mass), and ${s}_{1}, {s}_{2}, {s}_{3}$ are the sides of the triangle. We compute the $T$-matrix element for three such fermions colliding at low energy in terms of $D$ in the absence of two-body interactions. When the interactions are weak, we calculate $D$ approximately using the Born expansion. We also analyze the energy shift of three two-component fermions in a large periodic cube due to $D$ and generalize this result to the many-fermion system. $D$ also determines the three-body recombination rates in two-component Fermi gases, and we calculate the three-body recombination rates in terms of $D$ and the density and temperature of the gas.

arXiv:2501.05194Physical Review AMay 22, 20251 citation

D

called the three-body scattering hypervolume. We study the three-body wave function asymptotically when three fermions are far apart or one spin-$\ensuremath{\uparrow}$ (spin-$\ensuremath{\downarrow}$) fermion and one pair, formed by the other two fermions, are far apart and derive three asymptotic expansions of the wave function. The three-body scattering hypervolume

D

appears in the coefficients of such expansions at the order of ${B}^{\ensuremath{-}5}$, where

B={[({s}_{1}^{2}+{s}_{2}^{2}+{s}_{3}^{2})/2]}^{1/2}

is the hyperradius of the triangle formed by the three fermions (we assume that the three fermions have the same mass), and

{s}_{1}, {s}_{2}, {s}_{3}

are the sides of the triangle. We compute the

T

-matrix element for three such fermions colliding at low energy in terms of

D

in the absence of two-body interactions. When the interactions are weak, we calculate

D

approximately using the Born expansion. We also analyze the energy shift of three two-component fermions in a large periodic cube due to

D

and generalize this result to the many-fermion system.

D

also determines the three-body recombination rates in two-component Fermi gases, and we calculate the three-body recombination rates in terms of

D

and the density and temperature of the gas.