arXiv subjects

Aik-meng Kuah

Publications and source records attributed to Aik-meng Kuah.

6 recordsLinked to original sources

arXiv2009

Completely Positive Maps and Classical Correlations

We expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily. We characterize the correlations in the initial state in terms of its quantum discord [H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)]. We prove that initial states that have only classical correlations lead to completely positive reduced dynamics. The induced maps can be not completely positive when quantum correlations including, but not limited to, entanglement are present. We outline the implications of our results to quantum process tomography experiments.

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arXiv2009

How state preparation can affect a quantum experiment: Quantum process tomography for open systems

We study the effects of preparation of input states in a quantum tomography experiment. We show that maps arising from a quantum process tomography experiment (called process maps) differ from the well know dynamical maps. The difference between the two is due to the preparation procedure that is necessary for any quantum experiment. We study two preparation procedures, stochastic preparation and preparation by measurements. The stochastic preparation procedure yields process maps that are linear, while the preparations using von Neumann measurements lead to non-linear processes, and can only be consistently described by a bi-linear process map. A new process tomography recipe is derived for preparation by measurement for qubits. The difference between the two methods is analyzed in terms of a quantum process tomography experiment. A verification protocol is proposed to differentiate between linear processes and bi-linear processes. We also emphasize the preparation procedure will have a non-trivial effect for any quantum experiment in which the system of interest interacts with its environment.

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arXiv2005

Schmidt states and positivity of linear maps

Using pure entangled Schmidt states, we show that m-positivity of a map is bounded by the ranks of its negative Kraus matrices. We also give an algebraic condition for a map to be m-positive. We interpret these results in the context of positive maps as entanglement witnesses, and find that only 1-positive maps are needed for testing entanglement.

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arXiv2005

Extension maps

We define extension maps as maps that extend a system (through adding ancillary systems) without changing the state in the original system. We show, using extension maps, why a completely positive operation on an initially entangled system results in a non positive mapping of a subsystem. We also show that any trace preserving map, either positive or negative, can be decomposed in terms of an extension map and a completely positive map.

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arXiv2003

Manifold of density matrices

We show that the manifold of density matrices can be derived from CP^{N^2-1} by the action of SU(N). We give some preliminary observations on the structure of this manifold.

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arXiv2002

Dynamical maps and measurements

We show how a set of POVMs, expressed as a set of $μ$ linear maps, can be performed with a unitary transformation followed by a von-Neumann measurement with an ancillary system of no more than $μN^2$ dimensions. This result shows that all generalized linear transformations and measurements on density matrices can be performed by unitary transformations and von-Neumann measurements by coupling a suitably large ancillary system.

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