Abstract:
According to a fundamental result in quantum computing, any unitary
transformation on a composite system can be generated using so-called 2-local
unitaries that act only on two subsystems. Beyond its importance in quantum
computing, this result can also be regarded as a statement about the dynamics
of systems with local Hamiltonians: although locality puts various constraints
on the short-term dynamics, it does not restrict the possible unitary
evolutions that a composite system with a general local Hamiltonian can
experience after a sufficiently long time. Here we show that this universality
does not remain valid in the presence of conservation laws and global
continuous symmetries such as U(1) and SU(2). In particular, we show that
generic symmetric unitaries cannot be implemented, even approximately, using
local symmetric unitaries. Based on this no-go theorem, we propose a method for
experimentally probing the locality of interactions in nature. In the context
of quantum thermodynamics, our results mean that generic energy-conserving
unitary transformations on a composite system cannot be realized solely by
combining local energy-conserving unitaries on the components. We show how this
can be circumvented via catalysis.
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