Private Quantum Channels
... poses. If two superoperators E = f pi Ui j 1 i N g and E 0 = f p0i Ui0 j 1 i N 0 g are identical (E () = E 0 () for all ), then they are unitarily related in the following way [6, Theorem 8.2] (where we assume N N 0 and if N > N 0 we pad E 0 with zero operators to make E and E 0 of equa ...
... poses. If two superoperators E = f pi Ui j 1 i N g and E 0 = f p0i Ui0 j 1 i N 0 g are identical (E () = E 0 () for all ), then they are unitarily related in the following way [6, Theorem 8.2] (where we assume N N 0 and if N > N 0 we pad E 0 with zero operators to make E and E 0 of equa ...
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Universal computation by multi-particle quantum walk
... Theorem: An n-qubit, g-gate quantum circuit can be efficiently simulated by a multiparticle quantum walk of n+1 particles on a graph with poly(n,g) vertices. • In contrast, to simulate an n-qubit circuit using a single particle quantum walk [Childs 09] the graph must be exponentially large in n. • ...
... Theorem: An n-qubit, g-gate quantum circuit can be efficiently simulated by a multiparticle quantum walk of n+1 particles on a graph with poly(n,g) vertices. • In contrast, to simulate an n-qubit circuit using a single particle quantum walk [Childs 09] the graph must be exponentially large in n. • ...
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... * A « System » is an entity of the natural world that can be isolated well enough to carry properties with definite values, such as mass, charge, position... * Such properties are measured by using devices external to the system, and the complete specification of the measurement apparatus will be ca ...
... * A « System » is an entity of the natural world that can be isolated well enough to carry properties with definite values, such as mass, charge, position... * Such properties are measured by using devices external to the system, and the complete specification of the measurement apparatus will be ca ...
