Proposal of an experimentally accessible measure of many-fermion entanglement

We propose a measure of interaction-induced ground state entanglement in many-fermion systems that is experimentally accessible. It is formulated in terms of cross-correlations of currents through resonant fermion levels weakly coupled to the probed system. The proposed entanglement measure vanishes in the absence of many-body interactions and it is related to measures of occupation number entanglement. We evaluate it for two examples of interacting electronic nanostructures.Comment: 5 pages, 3 figures, published versio

Dephasing of entangled electron-hole pairs in a degenerate electron gas

A tunnel barrier in a degenerate electron gas was recently discovered as a source of entangled electron-hole pairs. Here, we investigate the loss of entanglement by dephasing. We calculate both the maximal violation E_max of the Bell inequality and the degree of entanglement (concurrence) C. If the initially maximally entangled electron-hole pair is in a Bell state, then the Bell inequality is violated for arbitrary strong dephasing. The same relation E_max=2\sqrt{1+C^{2}} then holds as in the absence of dephasing. More generally, for a maximally entangled superposition of Bell states, the Bell inequality is satisfied for a finite dephasing strength and the entanglement vanishes for somewhat stronger (but still finite) dephasing strength. There is then no one-to-one relation between E_max and C.Comment: 7 pages with 3 figures, special style file included; To appear in a special issue on "Quantum Computation at the Atomic Scale" in Turkish Journal of Physic

Temperature dependent third cumulant of tunneling noise

Poisson statistics predicts that the shot noise in a tunnel junction has a temperature independent third cumulant e^2\I, determined solely by the mean current I. Experimental data, however, show a puzzling temperature dependence. We demonstrate theoretically that the third cumulant becomes strongly temperature dependent and may even change sign as a result of feedback from the electromagnetic environment. In the limit of a noninvasive (zero-impedance) measurement circuit in thermal equilibrium with the junction, we find that the third cumulant crosses over from e^2/I at low temperatures to -e^2/I at high temperatures.Comment: 4 pages including 2 figure

Feedback of the electromagnetic environment on current and voltage fluctuations out of equilibrium

A theory is presented for low-frequency current and voltage correlators of a mesoscopic conductor embedded in a macroscopic electromagnetic environment. This Keldysh field theory evaluated at its saddle-point provides the microscopic justification for our earlier phenomenological calculation (using the cascaded Langevin approach). The nonlinear feedback from the environment mixes correlators of different orders, which explains the unexpected temperature dependence of the third moment of tunneling noise observed in a recent experiment. At non-zero temperature, current and voltage correlators of order three and higher are no longer linearly related. We show that a Hall bar measures voltage correlators in the longitudinal voltage and current correlators in the Hall voltage. We go beyond the saddle-point approximation to consider the environmental Coulomb blockade. We derive that the leading order Coulomb blockade correction to the n-th cumulant of current fluctuations is proportional to the voltage derivative of the (n+1)-th cumulant, generalizing to any n the earlier results for n=1,2.Comment: 12 pages, 8 figure

Charge detection enables free-electron quantum computation

It is known that a quantum computer operating on electron-spin qubits with single-electron Hamiltonians and assisted by single-spin measurements can be simulated efficiently on a classical computer. We show that the exponential speed-up of quantum algorithms is restored if single-charge measurements are added. These enable the construction of a CNOT (controlled NOT) gate for free fermions, using only beam splitters and spin rotations. The gate is nearly deterministic if the charge detector counts the number of electrons in a mode, and fully deterministic if it only measures the parity of that number.Comment: 5 pages including 3 figure