564 research outputs found
Exact and Efficient Simulation of Concordant Computation
Concordant computation is a circuit-based model of quantum computation for
mixed states, that assumes that all correlations within the register are
discord-free (i.e. the correlations are essentially classical) at every step of
the computation. The question of whether concordant computation always admits
efficient simulation by a classical computer was first considered by B. Eastin
in quant-ph/1006.4402v1, where an answer in the affirmative was given for
circuits consisting only of one- and two-qubit gates. Building on this work, we
develop the theory of classical simulation of concordant computation. We
present a new framework for understanding such computations, argue that a
larger class of concordant computations admit efficient simulation, and provide
alternative proofs for the main results of quant-ph/1006.4402v1 with an
emphasis on the exactness of simulation which is crucial for this model. We
include detailed analysis of the arithmetic complexity for solving equations in
the simulation, as well as extensions to larger gates and qudits. We explore
the limitations of our approach, and discuss the challenges faced in developing
efficient classical simulation algorithms for all concordant computations.Comment: 16 page
Distinguishing multi-partite states by local measurements
We analyze the distinguishability norm on the states of a multi-partite
system, defined by local measurements. Concretely, we show that the norm
associated to a tensor product of sufficiently symmetric measurements is
essentially equivalent to a multi-partite generalisation of the non-commutative
2-norm (aka Hilbert-Schmidt norm): in comparing the two, the constants of
domination depend only on the number of parties but not on the Hilbert spaces
dimensions.
We discuss implications of this result on the corresponding norms for the
class of all measurements implementable by local operations and classical
communication (LOCC), and in particular on the leading order optimality of
multi-party data hiding schemes.Comment: 18 pages, 6 figures, 1 unreferenced referenc
Asymptotic entanglement transformation between W and GHZ states
We investigate entanglement transformations with stochastic local operations
and classical communication (SLOCC) in an asymptotic setting using the concepts
of degeneration and border rank of tensors from algebraic complexity theory.
Results well-known in that field imply that GHZ states can be transformed into
W states at rate 1 for any number of parties. As a generalization, we find that
the asymptotic conversion rate from GHZ states to Dicke states is bounded as
the number of subsystems increase and the number of excitations is fixed. By
generalizing constructions of Coppersmith and Winograd and by using monotones
introduced by Strassen we also compute the conversion rate from W to GHZ
states.Comment: 11 page
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