Abstract-In this paper, we show that the conditional min-entropy Hmin(AjB) of a bipartite state AB is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the B-part of AB are allowed. In the special case where A is classical, this overlap corresponds to the probability of guessing A given B. In a similar vein, we connect the conditional max-entropy H max (AjB) to the maximum fidelity of AB with a product state that is completely mixed on A. In the case where A is classical, this corresponds to the security of A when used as a secret key in the presence of an adversary holding B.Because min-and max-entropies are known to characterize information-processing tasks such as randomness extraction and state merging, our results establish a direct connection between these tasks and basic operational problems. For example, they imply that the (logarithm of the) probability of guessing A given B is a lower bound on the number of uniform secret bits that can be extracted from A relative to an adversary holding B.Index Terms-Entropy measures, max-entropy, min-entropy, operational interpretations, quantum information theory, quantum hypothesis testing, singlet fraction, single-shot information theory.

Anaerobically treated sewage sludge was found to contain extraordinarily high concentrations of 4-nonylphenol, a metabolite derived from nonionic surfactants of the nonylphenol polyethoxylate type. Concentrations in activated sewage sludge, in mixed primary and secondary sludge, and in aerobically stabilized sludge were substantially lower, suggesting that the formation of 4-nonylphenol is favored under mesophilic anaerobic conditions. Because 4-nonylphenol may be highly toxic to aquatic life, further research is needed on the fate of 4-nonylphenol after sludge is disposed of in the environment.

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Abstract. We derive a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and can be applied in various quantum-cryptographic settings. Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit Commitment are presented and the uncertainty relation is used to prove the security of these protocols in the boundedquantum-storage model according to new strong security definitions. As another application, we consider the realistic setting of Quantum Key Distribution (QKD) against quantum-memory-bounded eavesdroppers. The uncertainty relation allows to prove the security of QKD protocols in this setting while tolerating considerably higher error rates compared to the standard model with unbounded adversaries. For instance, for the six-state protocol with one-way communication, a bit-flip error rate of up to 17% can be tolerated (compared to 13% in the standard model). Our uncertainty relation also yields a lower bound on the min-entropy key uncertainty against known-plaintext attacks when quantum ciphers are composed. Previously, the key uncertainty of these ciphers was only known with respect to Shannon entropy.

The investigated contaminants occur at quantitatively measurable but varying concentrations in municipal wastewaters and in the Glatt River reflecting their ubiquitous input into wastewaters and their different behaviour during biological wastewater treatment.

The Leftover Hash Lemma states that the output of a two-universal hash function applied to an input with sufficiently high entropy is almost uniformly random. In its standard formulation, the lemma refers to a notion of randomness that is (usually implicitly) defined with respect to classical side information. Here, we prove a (strictly) more general version of the Leftover Hash Lemma that is valid even if side information is represented by the state of a quantum system. Furthermore, our result applies to arbitrary δ-almost two-universal families of hash functions. The generalized Leftover Hash Lemma has applications in cryptography, e.g., for key agreement in the presence of an adversary who is not restricted to classical information processing.

We show how to implement cryptographic primitives based on the realistic assumption that quantum storage of qubits is noisy. We thereby consider individual-storage attacks, i.e. the dishonest party attempts to store each incoming qubit separately. Our model is similar to the model of bounded-quantum storage, however, we consider an explicit noise model inspired by present-day technology. To illustrate the power of this new model, we show that a protocol for oblivious transfer (OT) is secure for any amount of quantum-storage noise, as long as honest players can perform perfect quantum operations. Our model also allows the security of protocols that cope with noise in the operations of the honest players and achieve more advanced tasks such as secure identification.Traditional cryptography is concerned with the secure and reliable transmission of messages. With the advent of widespread electronic communication new cryptographic tasks have become increasingly important. Examples of such tasks are secure identification, electronic voting, online auctions, contract signing and other applications where the protocol participants do not necessarily trust each other. It is well-known that almost all these interesting tasks are impossible to realize without any restrictions on the participating players, neither classically nor with the help of quantum communication [8]. It is therefore an important task to come up with a cryptographic model which restricts the capabilities of adversarial players and in which these tasks become feasible. It turns out that all such two-party protocols can be based on a simple primitive called 1-2 Oblivious Transfer [1] (1-2 OT), first introduced in [3,4,5]. Hence, 1-2 OT is commonly used to provide a "proof of concept" for the universal power of a new model. In 1-2 OT, the sender Alice starts off with two bit strings S 0 and S 1 , and the receiver Bob holds a choice bit C. The protocol allows Bob to retrieve S C in such a way that Alice does not learn any information about C (thus, Bob cannot simply ask for S C ). At the same time, Alice must be ensured that Bob only learns S C , and no information about the other string S 1−C (thus, Alice cannot simply send him both S 0 and S 1 ). A 1-2 OT protocol is called unconditionally secure when neither Alice nor Bob can break these conditions, even when given unlimited resources.In this letter, we propose a cryptographic model based on current practical and near-future technical limitations, namely that quantum storage is noisy. Thus the presence of noise, the very problem that makes it so hard to implement a quantum computer, can actually be turned to our advantage. Recently it was shown that secure OT is possible when the receiver Bob has a lim- * wehner@caltech.edu † c.schaffner@cwi.nl ‡ bterhal@gmail.com ited amount of quantum memory [13,14] at his disposal. Within this 'bounded-quantum-storage model' OT can be implemented securely as long as a dishonest receiver Bob can store at most n/4−O(1) qubits coherently, where n is the number of qubits ...

The complexing agents benzotriazole (BT) and tolyltriazole (TT) are not only widely applied as anticorrosives, e.g., in aircraft deicer and anti-icer fluid (ADAF), but they are also used for so-called silver protection in dishwasher detergents. Due to their low biodegradability and limited sorption tendency, BT and TT are only partly removed in wastewater treatment. Residual concentrations of BT and TT were determined in ambient surface waters in Switzerland including 7 rivers which have distinct water flows and receive treated wastewater effluents at various dilution ratios. A maximum BT concentration of 6.3 microg/L was found in the Glatt River, and a maximum mass flow of 277 kg BT per week was observed in the Rhine River. In most cases, TT was about a factor 5-10 less abundant. During winter 2003/4, BT mass flows at 2 locations in the lower stretch of the Glatt River clearly indicated the input from nearby Zurich airport, where BT was applied as an anticorrosive ADAF component. BT concentrations measured in the three lakes Greifensee, Lake Zurich, and Lake Geneva were approximately 1.2, 0.1-0.4, and 0.2 microg/L, respectively. The observed environmental occurrences indicate that BT and TT are ubiquitous contaminants in the aquatic environment and that they belong to the most abundant individual water pollutants.