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Interaction cost of nonlocal gates
G Vidal1, K Hammerer, J I Cirac
1Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria.
Physical Review Letters
|June 13, 2002
Summary
We introduce the interaction cost for nonlocal gates, quantifying the minimal time needed. This cost allows comparing quantum gates and reveals a partial order based on nonlocality in two-qubit systems.
Area of Science:
- Quantum Information Science
- Quantum Control Theory
Background:
- Nonlocal gates are crucial for quantum computation and information processing.
- Comparing the efficiency and resource requirements of different quantum gates is essential.
Purpose of the Study:
- To define and analyze the 'interaction cost' of nonlocal gates.
- To establish a framework for comparing nonlocal gates based on operational metrics.
- To investigate the structure of nonlocality in two-qubit systems.
Main Methods:
- Defining interaction cost as minimal interaction time with local unitary assistance.
- Deriving an analytical expression for interaction cost in two-qubit systems for any coupling Hamiltonian.
- Analyzing the resulting partial order on the set of nonlocal gates.
Main Results:
- The interaction cost provides an operationally meaningful way to compare any two nonlocal gates.
- An analytical expression for the interaction cost of any two-qubit unitary operation is derived.
- A partial order is established, comparing the degree of nonlocality between gates.
Conclusions:
- The interaction cost offers a novel metric for quantifying gate complexity and resource demands.
- The derived partial order provides a deeper understanding of nonlocality in quantum systems.
- This framework is applicable to optimizing quantum control and information processing protocols.