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arXiv:cond-mat/0307103 · Physical Review Letters

Quantum Teleportation by Particle-Hole Annihilation in the Fermi Sea

C. W. J. Beenakker, M. Kindermann

Published Feb 3, 2004• 51 citations
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Abstract

We point out that the mutual annihilation of an electron-hole pair at a tunnel barrier leads to teleportation of the state of the annihilated electron to a second, distant electron--if the latter was previously entangled with the annihilated hole. We propose an experiment, involving low-frequency noise measurements on a two-dimensional electron gas in a high magnetic field, to detect teleportation of electrons and holes in the two lowest Landau levels.

DOI
10.1103/physrevlett.92.056801

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We point out that the mutual annihilation of an electron-hole pair at a tunnel barrier leads to teleportation of the state of the annihilated electron to a second, distant electron--if the latter was previously entangled with the annihilated hole. We propose an experiment, involving low-frequency noise measurements on a two-dimensional electron gas in a high magnetic field, to detect teleportation of electrons and holes in the two lowest Landau levels.
I. Introduction (Preface, Exciton entanglers, Photon entanglers) II. Entanglement basics (Quantum versus classical correlations, Bell inequality, Entanglement measures for pure states, Entanglement measures for mixed states, Particle conservation, Phase reference) III. How to entangle free particles (Free bosons, Free fermions) IV. Spin versus orbital entanglement V. Entanglement detection by noise measurements (Tunneling regime, Beyond the tunneling regime, Full counting statistics) VI. Loss of entanglement by dephasing VII. Quantum entanglement pump VIII. Teleportation by electron-hole annihilation IX. Three-qubit entanglement X. The experimental challenge
Building on a previous proposal for the entanglement of electron-hole pairs in the Fermi sea, we show how three qubits can be entangled without using electron-electron interactions. As in the two-qubit case, this electronic scheme works even if the sources are in (local) thermal equilibrium---in contrast to the photonic analog. The three qubits are represented by four edge-channel excitations in the quantum Hall effect (two hole excitations plus two electron excitations with identical channel index). The entangler consists of an adiabatic point contact flanked by a pair of tunneling point contacts. The irreducible three-qubit entanglement is characterized by the tangle, which is expressed in terms of the transmission matrices of the tunneling point contacts. The maximally entangled Greenberger-Horne-Zeilinger (GHZ) state is obtained for channel-independent tunnel probabilities. We show how low-frequency noise measurements can be used to determine an upper and lower bound to the tangle. The bounds become tighter the closer the electron-hole state is to the GHZ state.
In a two-dimensional electron gas under a strong magnetic field, correlations generate emergent excitations distinct from electrons. It has been predicted that "composite fermions"--bound states of an electron with two magnetic flux quanta--can experience zero net magnetic field and form a Fermi sea. Using infinite-cylinder density matrix renormalization group numerical simulations, we verify the existence of this exotic Fermi sea, but find that the phase exhibits particle-hole symmetry. This is self-consistent only if composite fermions are massless Dirac particles, similar to the surface of a topological insulator. Exploiting this analogy, we observe the suppression of 2k(F) backscattering, a characteristic of Dirac particles. Thus, the phenomenology of Dirac fermions is also relevant to two-dimensional electron gases in the quantum Hall regime.
While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors ν and 1-ν are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.