Entanglement and deterministic quantum computing with one qubit

Abstract

The role of entanglement and quantum correlations in complex physical systems and quantum information processing devices has become a topic of intense study in the past two decades. In this work we present new tools for learning about entanglement and quantum correlations in dynamical systems where the quantum states are mixed and the eigenvalue spectrum is highly degenerate. We apply these results to the Deterministic quantum computing with one qubit (DQC1) computation model and show that the states generated in a DQC1 circuit have an eigenvalue structure that makes them difficult to entangle, even when they are relatively far from the completely mixed state. Our results strengthen the conjecture that it may be possible to find quantum algorithms that do not generate entanglement and yet still have an exponential advantage over their classical counterparts.

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Cited by in corpus (12)

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• Power of one non-clean qubit
• Noise-tolerant parity learning with one quantum bit
• Why should we care about quantum discord?
• The Transfer of Entanglement Negativity at the Onset of Interactions
• Separable Ball around any Full-Rank Multipartite Product State
• The Dynamics of Entropies at the Onset of Interactions
• Dephasing effects on quantum correlations and teleportation in presence of state dependent bath
• Separable ellipsoids around multipartite states
• Expressivity of deterministic quantum computation with one qubit
• Bayesian optimization of non-classical optomechanical correlations
• Extrapolated Quantum States, Void States, and a Huge Novel Class of Distillable Entangled States