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arXiv:1310.5640 · Physical Review B

Entanglement witnessing and quantum cryptography with nonideal ferromagnetic detectors

Waldemar Kłobus, Andrzej Grudka, Andreas Baumgartner, Damian Tomaszewski, Christian Schönenberger, J. Martinek

Published Mar 5, 2014• 47 citations
arXivHTMLPDF

Abstract

We investigate theoretically the use of nonideal ferromagnetic contacts as a means to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of $\ensuremath{\eta}>1/\sqrt{3}\ensuremath{\approx}58%$ required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell's inequality with $\ensuremath{\eta}>1/\sqrt[4]{2}\ensuremath{\approx}84%$. In addition, we discuss the impact of decoherence and noise on entanglement detection and apply the presented framework to a simple quantum cryptography protocol. Our results are directly applicable to a large variety of experiments.

DOI
10.1103/physrevb.89.125404

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•Jan 1, 2016•0 citations
We investigate theoretically the use of nonideal ferromagnetic contacts as a means to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of \ensuremathη>1/3\ensuremath≈58\ensuremath{\eta}>1/\sqrt{3}\ensuremath{\approx}58%\ensuremathη>1/3​\ensuremath≈58 required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell's inequality with \ensuremathη>1/24\ensuremath≈84\ensuremath{\eta}>1/\sqrt[4]{2}\ensuremath{\approx}84%\ensuremathη>1/42​\ensuremath≈84. In addition, we discuss the impact of decoherence and noise on entanglement detection and apply the presented framework to a simple quantum cryptography protocol. Our results are directly applicable to a large variety of experiments.
Entangled states are essential in basics quantum communication protocols and quantum cryptography.Ferromagnetic contacts can work as a spin detector, giving possibility of converting information about electron spin to the electric charge, and therefore, detection of entangled states with the electric current measurements is possible.Method of conrming entanglement with non-ideal detectors is presented, the impact of decoherence and noise on states and quality of entanglement is discussed.Entanglement witness (EW) operator method is compared with the CHSH inequalities approach.Required spin polarization for the EW is lower than for the CHSH inequalities.System with asymmetric spin polarizations of detectors was analyzed, including the CHSH inequalities and the EW method.
Entanglement between spatially separated electrons in nanoscale transport is a fundamental property, yet to be demonstrated experimentally. Here we propose and analyse theoretically the transport statistics of a generic spin entangler coupled to a hybrid quantum dot-ferromagnet detector system. We show that the full distribution of charges arriving at the ferromagnetic terminals provides complete information on the spin state of the particles emitted by the entangler. This provides means for spin entanglement detection via electrical current correlations, with optimal measurement strategies depending on the a priori knowledge of ferromagnet polarization and spin-flip rates in the detector dots. The scheme is exemplified by applying it to Andreev and triple dot entanglers.
The generation of spin-entangled electrons is an important prerequisite for future solid-state quantum technologies. Cooper pairs in a superconductor can be split into separate electrons in a spin-singlet state, however, detecting their entanglement remains an open experimental challenge. Proposals to detect the entanglement by violating a Bell inequality typically require a large number of current cross-correlation measurements, and not all entangled states can be detected in this way. Here, we instead formulate an entanglement witness that can detect the spin-entanglement using only three cross-correlation measurements of the currents in the outputs of a Cooper pair splitter. We identify the optimal measurement settings for witnessing the entanglement, and we illustrate the use of our entanglement witness with a realistic model of a Cooper pair splitter for which we evaluate the cross-correlations of the output currents. Specifically, we find that the entanglement of the spins can be detected even with a moderate level of decoherence. Our work thereby paves the way for an experimental detection of the entanglement produced by Cooper pair splitters.
The development of quantum computing in quantum dots systems requires highly ecient and continuous solidstate source of spatially separated spin-entangled electrons.One of the approaches is a use of double quantum dot system connected to superconducting lead, where Cooper pairs provide a source of naturally entangled electrons.Apart from the source, an useful tool for detection of quantum entanglement is needed.We present entanglement detection by the ferromagnetic electrodes using entanglement witness operator method and direct measurement of spin polarized current in the system.We investigate requirements that have to be fullled by ferromagnetic detectors.
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The work contained in this thesis deals with two closely related topics. Papers I-III deal with charge transport statistics in nanoscale devices to investigate the presence of entanglement in the constituent electrons. We identify the contributions of entangled electron pairs to the current cross-correlations as a signature of entanglement. Paper IV treats the electric control of a quantum dot based spin qubit via Electric Dipole Spin Resonance.In Paper I, we present a spin entanglement detection model in a hybrid nanoscale device, with a general entangler connected to a set of quantum dots and anti-collinear ferromagnetic contacts. Our model allows us to study the implications of a non-ideal detector in an entanglement detection scheme.In Paper II, we investigate a scheme for generating and detecting orbitally entangled states in a device consisting of six quantum dots. The underlying process which enables our proposed scheme is sufficiently fast, even for the rapidly decaying quantum coherence of orbital states defined in a solid.In Paper III, we investigate a minimal entanglement detection scheme based on measurements of current cross correlations. We find a significant reduction in the number of measurements required for an entanglement test.In Paper IV, we investigate the optimisation of electrically controlling an electron spin in a gate defined semiconductor quantum dot. Specifically, we study how the shape of the quantum dot together with the direction of an in-plane magnetic field affect the spin relaxation rate and frequency of the induced Rabi oscillations.