Maximum Confidence Quantum Measurements

We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result. For linearly dependent sets an analogous measurement is one which allows us to be as confident as possible that when a given state is identified on the basis of the measurement result, it is indeed the correct state.Comment: 4 pages, 2 figure

A class of unambiguous state discrimination problems achievable by separable measurements but impossible by local operations and classical communication

We consider an infinite class of unambiguous quantum state discrimination problems on multipartite systems, described by Hilbert space $\cal{H}$, of any number of parties. Restricting consideration to measurements that act only on $\cal{H}$, we find the optimal global measurement for each element of this class, achieving the maximum possible success probability of $1/2$ in all cases. This measurement turns out to be both separable and unique, and by our recently discovered necessary condition for local quantum operations and classical communication (LOCC), it is easily shown to be impossible by any finite-round LOCC protocol. We also show that, quite generally, if the input state is restricted to lie in $\cal{H}$, then any LOCC measurement on an enlarged Hilbert space is effectively identical to an LOCC measurement on $\cal{H}$. Therefore, our necessary condition for LOCC demonstrates directly that a higher success probability is attainable for each of these problems using general separable measurements as compared to that which is possible with any finite-round LOCC protocol.Comment: Version 2 has new title along with an added discussion about using an enlarged Hilbert space and why this is not helpfu

Coherent pulse implementations of quantum cryptography protocols resistant to photon number splitting attacks

A new class of quantum cryptography (QC) protocols that are robust against the most general photon number splitting attacks in a weak coherent pulse implementation has been recently proposed. In this article we give a quite exhaustive analysis of several eavesdropping attacks on these schemes. The eavesdropper (Eve) is supposed to have unlimited technological power while the honest parties (Alice and Bob) use present day technology, in particular an attenuated laser as an approximation of a single-photon source. They exploit the nonorthogonality of quantum states for decreasing the information accessible to Eve in the multi-photon pulses accidentally produced by the imperfect source. An implementation of some of these protocols using present day technology allow for a secure key distribution up to distances of $\sim$ 150 km. We also show that strong-pulse implementations, where a strong pulse is included as a reference, allow for key distribution robust against photon number splitting attacks.Comment: 16 pages, 11 figure

Zero-Error Attacks and Detection Statistics in the Coherent One-Way Protocol for Quantum Cryptography

This is a study of the security of the Coherent One-Way (COW) protocol for quantum cryptography, proposed recently as a simple and fast experimental scheme. In the zero-error regime, the eavesdropper Eve can only take advantage of the losses in the transmission. We consider new attacks, based on unambiguous state discrimination, which perform better than the basic beam-splitting attack, but which can be detected by a careful analysis of the detection statistics. These results stress the importance of testing several statistical parameters in order to achieve higher rates of secret bits

Optimal signal states for quantum detectors

Quantum detectors provide information about quantum systems by establishing correlations between certain properties of those systems and a set of macroscopically distinct states of the corresponding measurement devices. A natural question of fundamental significance is how much information a quantum detector can extract from the quantum system it is applied to. In the present paper we address this question within a precise framework: given a quantum detector implementing a specific generalized quantum measurement, what is the optimal performance achievable with it for a concrete information readout task, and what is the optimal way to encode information in the quantum system in order to achieve this performance? We consider some of the most common information transmission tasks - the Bayes cost problem (of which minimal error discrimination is a special case), unambiguous message discrimination, and the maximal mutual information. We provide general solutions to the Bayesian and unambiguous discrimination problems. We also show that the maximal mutual information has an interpretation of a capacity of the measurement, and derive various properties that it satisfies, including its relation to the accessible information of an ensemble of states, and its form in the case of a group-covariant measurement. We illustrate our results with the example of a noisy two-level symmetric informationally complete measurement, for whose capacity we give analytical proofs of optimality. The framework presented here provides a natural way to characterize generalized quantum measurements in terms of their information readout capabilities.Comment: 13 pages, 1 figure, example section extende

Sequential Discrimination Between Non-Orthogonal Quantum States

The problem of discriminating between non-orthogonal states is one that has generated a lot of interest. This basic formalism is useful in many areas of quantum information. It serves as a fundamental basis for many quantum key distribution schemes, it functions as an integral part of other quantum algorithms, and it is useful in experimental settings where orthogonal states are not always possible to generate. Additionally, the discrimination problem reveals important fundamental properties, and is intrinsically related to entanglement. In this thesis, the focus is on exploring the problem of sequentially discriminating between non-orthogonal states. In the simplest version these schemes, Alice sends one of two known pure states to Bob who performs a non-optimal discrimination procedure such that the post measurement states resulting from his measurement can then be discriminated by a third participant, Charlie. In these schemes, the goal is to optimize the joint probability of both Bob and Charlie succeeding. In devising such a scheme, there are several different criteria that can be prioritized. The most basic scheme, referred to as Minimum Error (ME) discrimination, prioritizes Bob\u27s and Charlie\u27s abilities to successfully determine which state was sent by Alice. In this scheme, Bob and Charlie each set up two detectors and based on the result from the detector they make a guess as to which state was sent. For instance, if Bob registers a click in his first detector, he concludes that Alice sent the first state. As each detector has some probability to produce a result for either incoming result, Bob and Charlie optimize their joint probability of success by optimizing the probability that each detector will fire when the correlated state is sent by Alice. Another possible scheme, referred to as Unambiguous Discrimination (UD), prioritizes Bob\u27s and Charlie\u27s ability to correctly determine the state sent by Alice. In this scheme, Bob and Charlie each set up three detectors, where if a result is obtained from the first two detectors Bob or Charlie can determine with certainty which state was sent by Alice. One final setup, referred to as Discrimination with a Fixed Rate of Inconclusive Outcome, is a combination of the previous two schemes, where Bob and Charlie maximize their probability of successfully determining the state sent by Alice where they allow some fixed probability that they will not be able to determine which state Alice sent. This fixed inconclusive probability allows Bob and Charlie to control how much they prioritize correctly determining the state that was sent, as in the Unambiguous Discrimination, versus prioritizing successfully determining the state sent by Alice, as in Minimum Error discrimination. One final topic that will be discussed by this thesis is Quantum Retrodiction. Quantum Retrodiction applies an alternate perspective on the communication protocol between Alice and Bob. In the predictive model, Alice calculates the probability that Bob gets a specific measurement result given that she prepares her system in a specific state. In the retrodictive model, Bob calculates the probability that Alice prepared her system in a specific state given the result of his measurement. This alternate perspective on the communication procedure gives new a new understanding and new tools for approaching the problem of state discrimination, as exemplified by applying the retrodictive formalism to unambiguous discrimination

Optimum detection for extracting maximum information from symmetric qubit sets

We demonstrate a class of optimum detection strategies for extracting the maximum information from sets of equiprobable real symmetric qubit states of a single photon. These optimum strategies have been predicted by Sasaki et al. [Phys. Rev. A{\bf 59}, 3325 (1999)]. The peculiar aspect is that the detections with at least three outputs suffice for optimum extraction of information regardless of the number of signal elements. The cases of ternary (or trine), quinary, and septenary polarization signals are studied where a standard von Neumann detection (a projection onto a binary orthogonal basis) fails to access the maximum information. Our experiments demonstrate that it is possible with present technologies to attain about 96% of the theoretical limit.Comment: 10 pages, 11 figures, to be submitted to Phys. Rev. A Converted to REVTeX4 format, and a few other minor modifications according to the comments from PRA referre