Entanglement and the power of one qubit

By Animesh Datta, Steven T. Flammia, Carlton M. Caves. 2005

304 citations recorded by the source corpus.

The ``power of one qubit'' refers to a computational model that has access to only one pure bit of quantum information, along with $n$ qubits in the totally mixed state. This model, though not as powerful as a pure-state quantum computer, is capable of performing some computational tasks exponentially faster than any known classical algorithm. One such task is to estimate with fixed accuracy the normalized trace of a unitary operator that can be implemented efficiently in a quantum circuit. We show that circuits of this type generally lead to entangled states, and we investigate the amount of entanglement possible in such circuits, as measured by the multiplicative negativity. We show that the multiplicative negativity is bounded by a constant, independent of $n$, for all bipartite divisions of the $n+1$ qubits, and so becomes, when $n$ is large, a vanishingly small fraction of the maximum possible multiplicative negativity for roughly equal divisions. This suggests that the global nature of entanglement is a more important resource for quantum computation than the magnitude of the entanglement.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4f302197a4db57cdb6187134f9063cea06003663

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum-enhanced measurements without entanglement (2017, background): “…of onequbit” (Knill and Laflamme, 1998): With a set of qubits 32 of which only a single one is initially in a pure state, a quantum enhancement is already possible in quantum computation, providing evidence for an important role of quantum discord (Datta et al., 2005; Lanyon et al., 2008) (see Sec.”
The classical-quantum boundary for correlations: Discord and related measures (2011, methodology): “The estimate is independent of the input size n and the number of runs required for reaching a given accuracy is a quadratic function of the accuracy (Datta et al., 2005).”
Quantum circuits and low-degree polynomials over F2 (2016, background): “Flammia and Caves [13] to study the complexity of the “one clean qubit” model by expressing the trace of a unitary operator in terms of the number of zeroes of a degree-3 polynomial.”
Negative quasi-probability as a resource for quantum computation (2012, background): “…of quantum computation such as DQC1 (Knill and Laflamme 1998), algorithms that may be performed on highly mixed input states appear to be more powerful than classical computation even though there appears to be a negligible amount of entanglement in the underlying quantum system (Datta et al 2005).”
Quasi-probability representations of quantum theory with applications to quantum information science (2010, methodology): “In the DQC1 model, the bipartite split between the control qubit and the rest contains no entanglement and in Datta et al (2005) it was shown that there is a vanishingly small amount of entanglement across any other bipartite splitting.”
Corrigendum: Negative quasi-probability as a resource for quantum computation (2012, background): “Moreover, in alternative models of quantum computation such as DQC1 [31], algorithms that may be performed on highly-mixed input states appear to be more powerful than classical computation even though there appears to be a negligible amount of entanglement in the underlying quantum system [12].”