Mixed quantum state detection with inconclusive results

We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a sufficient condition for the scaled inverse measurement to maximize the probability of correct detection for the case in which the rate of inconclusive results exceeds a certain threshold. Using this condition we derive the optimal measurement for linearly independent pure-state sets, and for mixed-state sets with a broad class of symmetries. Specifically, we consider geometrically uniform (GU) state sets and compound geometrically uniform (CGU) state sets with generators that satisfy a certain constraint. We then show that the optimal measurements corresponding to GU and CGU state sets with arbitrary generators are also GU and CGU respectively, with generators that can be computed very efficiently in polynomial time within any desired accuracy by solving a semidefinite programming problem.Comment: Submitted to Phys. Rev.

A Package for the Implementation of Block Codes as Finite Automata

We have implemented a package that transforms concise algebraic descriptions of linear block codes into finite automata representations, and also generates decoders from such representations. The transformation takes a description of the code in the form of a k generator matrix over a field with q elements, representing a finite language containing q strings, and constructs a minimal automaton for the language from it, employing a well known algorithm. Next, from a decomposition of the minimal automaton into subautomata, it generates an overlayed automaton, and an e#cient decoder for the code using a new algorithm. A simulator for the decoder on an additive white Gaussian noise channel is also generated. This simulator can be used to run test cases for specific codes for which an overlayed automaton is available. Experiments on the well known Golay code indicate that the new decoding algorithm is considerably more e#cient than the traditional Viterbi algorithm run on the original automaton

Regular simplex fingerprints and their optimality properties

Abstract. This paper addresses the design of additive fingerprints that are maximally resilient against Gaussian averaging collusion attacks. The detector performs a binary hypothesis test in order to decide whether a user of interest is among the colluders. The encoder (fingerprint designer) is to imbed additive fingerprints that maximize the probability of detecting at least one of the colluders. Both the encoder and the attackers are subject to squared-error distortion constraints. We show that n-Simplex Fingerprints are optimal in sense of maximizing a geometric figure of merit for the detection test; these fingerprints outperform orthogonal fingerprints. They are also optimal in terms of maximizing the error exponent of the detection test, and maximizing the deflection criteria at the detector when the attacker’s noise is non-Gaussian.Reliable detection is guaranteed provided that the number of colluders K ≪ √ N, where N is the length of the host vector. Key words. Fingerprinting, Simplex codes, Error exponents.