49 research outputs found
Information-Theoretically Secure Voting Without an Honest Majority
We present three voting protocols with unconditional privacy and
information-theoretic correctness, without assuming any bound on the number of
corrupt voters or voting authorities. All protocols have polynomial complexity
and require private channels and a simultaneous broadcast channel. Our first
protocol is a basic voting scheme which allows voters to interact in order to
compute the tally. Privacy of the ballot is unconditional, but any voter can
cause the protocol to fail, in which case information about the tally may
nevertheless transpire. Our second protocol introduces voting authorities which
allow the implementation of the first protocol, while reducing the interaction
and limiting it to be only between voters and authorities and among the
authorities themselves. The simultaneous broadcast is also limited to the
authorities. As long as a single authority is honest, the privacy is
unconditional, however, a single corrupt authority or a single corrupt voter
can cause the protocol to fail. Our final protocol provides a safeguard against
corrupt voters by enabling a verification technique to allow the authorities to
revoke incorrect votes. We also discuss the implementation of a simultaneous
broadcast channel with the use of temporary computational assumptions, yielding
versions of our protocols achieving everlasting security
The cost of exactly simulating quantum entanglement with classical communication
We investigate the amount of communication that must augment classical local
hidden variable models in order to simulate the behaviour of entangled quantum
systems. We consider the scenario where a bipartite measurement is given from a
set of possibilities and the goal is to obtain exactly the same correlations
that arise when the actual quantum system is measured. We show that, in the
case of a single pair of qubits in a Bell state, a constant number of bits of
communication is always sufficient--regardless of the number of measurements
under consideration. We also show that, in the case of a system of n Bell
states, a constant times 2^n bits of communication are necessary.Comment: 9 pages, LaTeX, no figure
The Impossibility of Pseudo-Telepathy Without Quantum Entanglement
Imagine that Alice and Bob, unable to communicate, are both given a 16-bit
string such that the strings are either equal, or they differ in exactly 8
positions. Both parties are then supposed to output a 4-bit string in such a
way that these short strings are equal if and only if the original longer
strings given to them were equal as well. It is known that this task can be
fulfilled without failure and without communication if Alice and Bob share 4
maximally entangled quantum bits. We show that, on the other hand, they CANNOT
win the same game with certainty if they only share classical bits, even if it
is an unlimited number. This means that for fulfilling this particular
distributed task, quantum entanglement can completely replace communication.
This phenomenon has been called pseudo-telepathy. The results of this paper
complete the analysis of the first proposed game of this type between two
players.Comment: 6 pages, LaTe
The GHZ state in secret sharing and entanglement simulation
In this note, we study some properties of the GHZ state. First, we present a
quantum secret sharing scheme in which the participants require only classical
channels in order to reconstruct the secret; our protocol is significantly more
efficient than the trivial usage of teleportation. Second, we show that the
classical simulation of an n-party GHZ state requires at least n log n - 2n
bits of communication. Finally, we present a problem simpler than the complete
simulation of the multi-party GHZ state, that could lead to a no-go theorem for
GHZ state simulation.Comment: 5 page