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Random Access Codes is an information task that has been extensively studied and found many applications in quantum information. In this scenario, Alice receives an n-bit string x, and wishes to encode x into a quantum state ρ x , such that Bob, when receiving the state ρ x , can choose any bit i ∈ [n] and recover the input bit x i with high probability.(More)
A resolution proof or a derivation of the empty clause from a set of clauses S = {<italic>C</italic><subscrpt>1</subscrpt>, <italic>C</italic><subscrpt>2</subscrpt>, &#8230;, <italic>C<subscrpt>k</subscrpt></italic>} is called a <italic>tree resolution</italic> if no clause <italic>C<subscrpt>i</subscrpt></italic> is used in more than one resolvent. We show(More)
Let the randomized query complexity of a relation for error probability ǫ be denoted by Rǫ(·). We prove that for any relation f ⊆ {0, 1} × R and Boolean function g : {0, 1} → {0, 1}, R1/3(f ◦g ) = Ω(R4/9(f) ·R1/2−1/n4(g)), where f ◦g n is the relation obtained by composing f and g. We also show that R1/3 (
We show that for any (partial) query function f : {0, 1} n → {0, 1}, the randomized communication complexity of f composed with Index n m (with m = poly(n)) is at least the random-ized query complexity of f times log n. Here Index m : [m] × {0, 1} m → {0, 1} is defined as Index m (x, y) = y x (the xth bit of y). Our proof follows on the lines of Raz and(More)
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