We investigate the effects of the orientation of the magnetic field and the orientation of a quantum dot, with respect to crystallographic coordinates, on the quality of an electrically controlled qubit realized in a gated semiconductor quantum dot. We find that, due to the anisotropy of the spin-orbit interactions, by varying the two orientations it is possible to tune the qubit in the sense of optimizing the ratio of its couplings to phonons and to a control electric field. We find conditions under which such optimal setup can be reached by solely reorienting the magnetic field, and when a specific positioning of the dot is required. We also find that the knowledge of the relative sign of the spin-orbit interaction strengths allows to choose a robust optimal dot geometry, with the dot main axis along [110], or [110], where the qubit can be always optimized by reorienting the magnetic field.

Despite great efforts, an unambiguous demonstration of entanglement of mobile electrons in solid state conductors is still lacking. Investigating theoretically a generic entangler-detector setup, we here show that a witness of entanglement between two flying electron qubits can be constructed from only two current cross correlation measurements, for any nonzero detector efficiencies and non-collinear polarization vectors. We find that all entangled pure states, but not all mixed ones, can be detected with only two measurements, except the maximally entangled states, which require three. Moreover, detector settings for optimal entanglement witnessing are presented. [19,20], even when the number of entangled particles is large [21].The prospects of few-measurement entanglement detection make witnesses particularly interesting for flying qubits in solid state conductors, where an unambiguous demonstration of entanglement is still lacking. Here, detection schemes for spatially separated, spin [22,23] or orbitally [24][25][26][27] entangled, electrons have been proposed based on experimentally accessible current cross correlations [28]. However, the required set of measurements, with different, non-collinear detector settings and correlations between two or more pairs of detector terminals, are experimentally highly challenging. Aiming for less demanding measurements, works [29,30] on witnesses have proposed schemes with only two or three settings and less than ten cross correlations, allowing detection of certain classes of entangled states. Yet, two fundamental questions remain unanswered: (i) What is the minimum number of current cross correlation measurements needed for an entanglement witness? (ii) Which entangled states can be detected by such a witness?Here we answer these two questions within a generic solid state entangler-detector model, see Fig. 1. We find that only two cross correlation measurements -two detector settings with one measurement per setting -are sufficient to constitute a witness. Moreover, we show that all entangled pure (but not all mixed) states can be detected by the witness, except the maximally entangled, which require three measurements. In addition, the

Recent experiments have demonstrated sub decoherence time control of individual single-electron orbital qubits. Here we propose a quantum dot based scheme for generation and detection of pairs of orbitally entangled electrons on a timescale much shorter than the decoherence time. The electrons are entangled, via two-particle interference, and transferred to the detectors during a single cotunneling event, making the scheme insensitive to charge noise. For sufficiently long detector dot lifetimes, cross-correlation detection of the dot charges can be performed with real-time counting techniques, opening up for an unambiguous short-time Bell inequality test of orbital entanglement.PACS numbers: 73.63. Kv, 03.65.Ud, 03.67.Bg, 73.50.Td The concept of quantum entanglement has ever since its inception attracted much attention. Initially questioned because of its nonlocal properties, violating local realism [1, 2], entanglement has over the past decades emerged as an indispensable resource for quantum information processing [3]. Spurred by proposals for electronic spin-based quantum computing [4,5], spin qubit experiments [6,7] and demonstrations of long spin decoherence times [8], large efforts have been devoted to investigations of spin entanglement in nanostructures. Recent experimental progress comprises entanglement of singleelectron [9] and two-electron [10] spin qubits and splitting [11][12][13][14] of spin-singlet Cooper pairs in hybrid superconducting systems.In contrast to spin, entanglement between electronic orbital degrees of freedom [15,16], such as charge states in quantum dots [17] or edge channels in quantum Hall systems [18][19][20], has received limited attention. In particular, orbital entanglement has not been demonstrated experimentally. The key reason is arguably that superpositions of orbital states are sensitive to charge noise, resulting in short decoherence times, of the order of nanoseconds [21][22][23][24]. This has led to the widespread view that, despite all-electrical quantum state control and read-out, electronic orbital degrees of freedom cannot be harnessed for quantum information processing. Very recently this view was contested by demonstrations of fast, coherent operations of single-electron orbital qubits on the picosecond timescale [25][26][27], several orders of magnitude shorter than the decoherence time. These experiments motivate renewed efforts on orbital-based quantum information processing and call for novel schemes to generate and detect orbital entanglement on timescales well below the decoherence time.Here we propose such an entanglement scheme, based on coherent electron cotunneling [28] in a quantum dot system, see Fig. 1. During the cotunneling event, of the order of picoseconds [29,30], the electrons are entangled via two-particle interference [18,31] and simultaneously transferred to the detectors, fully preserving coherence [32,33]. We show, based on the full transfer statistics [34,35], that the entanglement can conveniently be detected by violating a Bell ine...

We study the production of spatially separated entangled electrons in ferromagnetic leads from Cooper pairs in a superconducting lead. We give a complete description of the elementary charge transfer processes, i) transfer of Cooper pairs out of the superconductor by Andreev reflection and ii) distribution of the entangled quasiparticles among the ferromagnetic leads, in terms of their statistics. The probabilities that entangled electrons flow into spatially separated leads are completely determined by experimentally measurable conductances and polarizations. Finally, we investigate how currents, noise and cross correlations are affected by transport of entangled electrons. [2,3,4,5]. One of the challenges is to prevent processes where pairs of entangled particles reach the same lead, i.e. are not spatially separated. Electrons from Cooper pairs are entangled in spin and energy space, and separation of pairs into different leads using ferromagnets or quantum dots has been suggested [3]. Upon filtering, only the spin or energy part of the two-particle wave function collapses, depending on whether ferromagnets or quantum dots are used. Respectively, energy or spin entanglement remains [4]. Here we consider separation by ferromagnets.Solid state entanglers have been analyzed in Refs. [2,3,4,5] in terms of currents, noise and cross correlations. A more direct approach, describing the elementary charge transfer processes in terms of experimentally controllable parameters is certainly desirable. We demonstrate how this is possible through the full distribution of current fluctuations, the full counting statistics (FCS), of the solid state entangler [6,7,8]. The FCS provides complete information about currents, noise, cross correlations and higher cumulants, and even more importantly, allows direct access to the probability for transfer of charge between different parts of the device.We consider the singlet superconductor-ferromagnet (S-F) device shown in Fig. 1. A normal metal cavity (c) is connected to one superconducting terminal and several ferromagnetic terminals via tunnel junctions. The cavity is under the influence of proximity effect. In this device, charge transport occurs via two processes: i) Transfer of Cooper pairs out of the superconductor by Andreev reflection and ii) distribution of the entangled quasi- particles among the ferromagnetic leads. The distribution can occur via Direct Andreev (DA) reflection, where a entangled pair is transferred into lead F n or crossed Andreev reflection (CA), where each particle of the entangled pair is transferred into spatially separated leads F m and F n (n = m). CA produces spatially separated entangled electrons. Since the ferromagnetic terminals are at the same voltage and we consider zero temperature, there is no direct electron transport between the ferromagnetic terminals [9].Our general results for the counting statistics show that the processes i) and ii) are independent and therefore the statistics can be factorized. This novel factorization and the probab...

We investigate, theoretically, charge-noise-induced spin dephasing of a hole confined in a quasi-twodimensional silicon quantum dot. Central to our treatment is accounting for higher-order corrections to the Luttinger Hamiltonian. Using experimentally reported parameters, we find that the new terms give rise to sweet spots for the hole-spin dephasing, which are sensitive to device details: dot size and asymmetry, growth direction, and applied magnetic and electric fields. Furthermore, we estimate that the dephasing time at the sweet spots is boosted by several orders of magnitude, up to on the order of milliseconds.