By Dimitris G. Angelakis, Matthias Christandl, Artur Ekert, Alastair Kay, Sergei Kulik

The Antikythera mechanism used to be most likely the world’s first ‘analog computing device’ — a cosmopolitan machine for calculating the motions of stars and planets. This striking meeting of greater than 30 gears with a differential mechanism, made on Rhodes or Cos within the first century B.C., revised the view of what the traditional Greeks have been in a position to developing at the moment. A related point of engineering didn’t develop into frequent till the economic revolution approximately millennia later. This number of papers offers a very good assessment of the present state of the art of quantum details technological know-how. we don't understand how a quantum Antikythera will seem like yet all we all know is that tips to are expecting the longer term is to create it. From the viewpoint of the long run, it could be that the true laptop age has no longer but even all started.

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The work is partially supported by Polish Ministry of Scientiﬁc Research and Information Technology grant under the (solicited) project no. PBZ-MIN008/P03/2003 and by EC grant: RESQ, contract no. IST-2001-37559. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] A. Ekert, Phys. Rev. Lett. 67, 661 (1991). C. H. Bennett, G. Brassard, and N. D. Mermin, Phys. Rev. Lett. 68, 557 (1992). B. M. Terhal, IBM J. Res. Dev. 48, 71 (2004). D. Deutsch, A. Ekert, R. Jozsa, C.

Conversely, let A be a subset of S(H) satisfying the criterion. Let ρ n be an arbitrary sequence in A. Since the unit ball in B(H) is compact in the weak operator topology [2], there exists a subsequence ρ nk converging to a positive operator ρ ∗ in this topology. We have Trρ∗ ≤ lim inf Trρnk = 1, k→∞ therefore to prove that ρ ∗ is a state it is sufﬁcient to show that Trρ∗ ≥ 1. Let ε > 0 and Pε be the corresponding projector. We have Trρ∗ ≥ TrPε ρ∗ = lim TrPε ρnk > 1 − ε, k→∞ where the equality follows from the fact that P ε has ﬁnite rank.

5) 22 P. Horodecki and R. Augusiak / On Quantum Cryptography with Bipartite Bound Entangled States The importance of such a class of operations follows from the fact that applied to a given state ABA B , U do not change its ccq state. , ˜ABE . ˜ABE = σ Now we deﬁne the central notion of the generalised approach provided in [9,10]. This is the notion of private state that has log d bits of secure key encoded in its AB part of d ⊗ d type). Deﬁnition 4. (pdit) Let ABA B is a density operator acting on the Hilbert space (A B ) (i = 0, .