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We propose a protocol that enables a dealer to share a quantum secret with n players using less than n quantum shares for several access structures. For threshold schemes we derived an expression that shows how many quantum shares can be saved in this scheme. Also, several features that are available for classical secret-sharing schemes ͑and previously not known to be possible for quantum secret-sharing͒ become available with this protocol.

In extension of the bit commitment task and following work initiated by Crépeau and Kilian, we introduce and solve the problem of characterising the optimal rate at which a discrete memoryless channel can be used for bit commitment. It turns out that the answer is very intuitive: it is the maximum equivocation of the channel (after removing trivial redundancy), even when unlimited noiseless bidirectional side communication is allowed. By a well-known reduction, this result provides a lower bound on the channel's capacity for implementing coin tossing, which we conjecture to be an equality.The method of proving this relates the problem to Wyner's wire-tap channel in an amusing way. We also discuss extensions to quantum channels.