22 research outputs found
Cloning by positive maps in von Neumann algebras
We investigate cloning in the general operator algebra framework in arbitrary
dimension assuming only positivity instead of strong positivity of the cloning
operation, generalizing thus results obtained so far under that stronger assumption.
The weaker positivity assumption turns out quite natural when considering cloning in
the general C∗-algebra framework
Quantum uniqueness
In the classical world one can construct two identical systems which have
identical behavior and give identical measurement results. We show this to be
impossible in the quantum domain. We prove that after the same quantum
measurement two different quantum systems cannot yield always identical
results, provided the possible measurement results belong to a non orthogonal
set. This is interpreted as quantum uniqueness - a quantum feature which has no
classical analog. Its tight relation with objective randomness of quantum
measurements is discussed.Comment: Presented at 4th Feynman festival, June 22-26, 2009, in Olomouc,
Czech Republic
Quantum Computing Without Wavefunctions: Time-Dependent Density Functional Theory for Universal Quantum Computation
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms
Quantum correlations with no causal order
The idea that events obey a definite causal order is deeply rooted in our
understanding of the world and at the basis of the very notion of time. But
where does causal order come from, and is it a necessary property of nature? We
address these questions from the standpoint of quantum mechanics in a new
framework for multipartite correlations which does not assume a pre-defined
global causal structure but only the validity of quantum mechanics locally. All
known situations that respect causal order, including space-like and time-like
separated experiments, are captured by this framework in a unified way.
Surprisingly, we find correlations that cannot be understood in terms of
definite causal order. These correlations violate a 'causal inequality' that is
satisfied by all space-like and time-like correlations. We further show that in
a classical limit causal order always arises, which suggests that space-time
may emerge from a more fundamental structure in a quantum-to-classical
transition.Comment: 13 pages, 5 figure