TY  - JOUR
A1  - Gross, David
A1  - Liu, Yi-Kai
A1  - Flammia, Steven T.
A1  - Becker, Stephen
A1  - Eisert, Jens
T1  - Quantum state tomography via compressed sensing
N2  - We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rdlog(2)d) measurement settings, compared to standard methods that require d(2) settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed.
Y1  - 2010
UR  - http://prl.aps.org/
U6  - https://doi.org/10.1103/Physrevlett.105.150401
SN  - 0031-9007
ER  - 
TY  - JOUR
A1  - Gross, David
A1  - Flammia, Steven T.
A1  - Eisert, Jens
T1  - Most quantum states are too entangled to be useful as computational resources
N2  - It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs a sufficient amount of entanglement for this speedup to be manifest. In measurement- based quantum computing, the need for a highly entangled initial state is particularly obvious. Defying this intuition, we show that quantum states can be too entangled to be useful for the purpose of computation, in that high values of the geometric measure of entanglement preclude states from offering a universal quantum computational speedup. We prove that this phenomenon occurs for a dramatic majority of all states: the fraction of useful n-qubit pure states is less than exp(-n(2)). This work highlights a new aspect of the role entanglement plays for quantum computational speedups.
Y1  - 2009
UR  - http://prl.aps.org/
U6  - https://doi.org/10.1103/Physrevlett.102.190501
SN  - 0031-9007
ER  -