Exploring entanglement resource in Si quantum dot systems with operational quasiprobability approach

Junghee Ryu and Hoon Ryu

Division of National Supercomputing, Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea

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Abstract

We characterize the quantum entanglement of the realistic two-qubit signals that are sensitive to charge noises. Our working example is the time response generated from a silicon double quantum dot (DQD) platform, where a single-qubit rotation and a two-qubit controlled-NOT operation are conducted sequentially in time to generate arbitrary entangled states. In order to characterize the entanglement of two-qubit states, we employ the marginal operational quasiprobability (OQ) approach that allows negative values of the probability function if a given state is entangled. While the charge noise, which is omnipresent in semiconductor devices, severely affects logic operations implemented in the DQD platform, causing huge degradation in fidelity of unitary operations as well as resulting two-qubit states, the pattern in the OQ-driven entanglement strength turns out to be quite invariant, indicating that the resource of quantum entanglement is not significantly broken though the physical system is exposed to noise-driven fluctuations in exchange interaction between quantum dots.

We characterize the entanglement of two quantum bits (qubits) states that are generated in a realistically sized silicon (Si) double quantum dot (DQD) platform. For arbitrary two-qubit states that are produced through conduction of a single qubit rotation followed by a controlled-X operation, we employ the marginal operational quasiprobability (OQ) function to directly quantify their entanglement resource. Here we show that the marginal OQ function, which can be constructed solely with directly measurable operators, can serve as a solid indicator of quantum entanglement even though a given state is contaminated too much with charge noises, since it characterizes the entanglement strength with reasonable accuracy and lower computing cost compared to the well-known negativity method that involves the full state tomography process. We also investigate how two-qubit states in a Si DQD system are affected by charge noises that are omnipresent in semiconductor devices. While we see that the noise drives huge degradation in fidelity, its effect on the entanglement resource turns out to be much weaker so more than 70% of resource can be retained for maximally entangled Bell states even in a strongly noisy condition where the state fidelity drops to around 20%.

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