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We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values (x, y) to (x, x⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2n)) can be expressed as compositions of these gates. We investigate the number of the above gates required to… (More)

- Charles H. Bennett, Gilles Brassard
- Theor. Comput. Sci.
- 2014

Entanglement purification protocols (EPP) and quantum errorcorrecting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a bipartite mixed state M ; with a QECC, an arbitrary quantum state |ξ〉 can be transmitted at some rate Q… (More)

- Charles H. Bennett, Ethan Bernstein, Gilles Brassard, Umesh V. Vazirani
- SIAM J. Comput.
- 1997

Recently a great deal of attention has been focused on quantum computation following a sequence of results [Bernstein and Vazirani, in Proc. 25th Annual ACM Symposium Theory Comput., 1993, pp. 11–20, SIAM J. Comput., 26 (1997), pp. 1411–1473], [Simon, in Proc. 35th Annual IEEE Symposium Foundations Comput. Sci., 1994, pp. 116–123, SIAM J. Comput., 26… (More)

An unknown quantum state ji can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical EPR correlations. To do so the sender, \Alice," and the receiver, \Bob," must prearrange the sharing of an EPR-correlated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum… (More)

- Charles H. Bennett, Gilles Brassard, Claude Crépeau, Ueli Maurer
- IEEE Trans. Information Theory
- 1995

~ This paper provides a general treatment of privacy amplification by public discussion, a concept introduced by Bennett, Brassard and Robert [l] for a special scenario. The results have applications to unconditionally-secure secret-key agreement protocols, quantum cryptography and to a non-asymptotic and constructive treatment of the secrecy capacity of… (More)

Some mathematical and natural objects (a random sequence, a sequence of zeros, a perfect crystal, a gas) are intuitively trivial, while others (e.g. the human body, the digits of π) contain internal evidence of a nontrivial causal history. We formalize this distinction by defining an object’s “logical depth” as the time required by a standard universal… (More)

- Charles H. Bennett, John Gill
- SIAM J. Comput.
- 1981

- Charles H. Bennett, Gilles Brassard, Jean-Marc Robert
- SIAM J. Comput.
- 1988

In this paper, we investigate how the use of a channel with perfect authenticity but no privacy can be used to repair the defects of a channel with imperfect privacy but no authenticity. More precisely, let us assume that Alice and Bob wish to agree on a secret random bit string, and have at their disposal an imperfect private channel and a perfect public… (More)

- Charles H. Bennett, François Bessette, Gilles Brassard, Louis Salvail, John A. Smolin
- Journal of Cryptology
- 1990

We describe results from an apparatus and protocol designed to implement quantum key distribution, by which two users, who share no secret information initially: (1) exchange a random quantum transmission, consisting of very faint flashes of polarized light; (2) by subsequent public discussion of the sent and received versions of this transmission estimate… (More)