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We establish fundamental upper bounds on the amount of secret key that can be extracted from quantum Gaussian states by using local Gaussian operations, local classical processing, and public communication. For one-way public communication or when two-way public communication is allowed but Alice and Bob first perform destructive local Gaussian measurements, we prove that the key is bounded by the Rényi-2 Gaussian entanglement of formation E_{F,2}^{G}. The saturation of this inequality for pure Gaussian states provides an operational interpretation of the Rényi-2 entropy of entanglement as the secret key rate of pure Gaussian states accessible with Gaussian operations and one-way communication. In the general setting of two-way communication and arbitrary interactive protocols, we argue that 2E_{F,2}^{G} still serves as an upper bound on the extractable key. We conjecture that the factor of 2 is spurious, suggesting that E_{F,2}^{G} coincides with the secret key rate of Gaussian states under Gaussian measurements and two-way public communication. We use these results to prove a gap between the secret key rates obtainable with arbitrary versus Gaussian operations. This gap is observed for states produced by sending one half of a two-mode squeezed vacuum through a pure loss channel, in the regime of sufficiently low squeezing or sufficiently high transmissivity. Finally, for a wide class of Gaussian states, including all two-mode states, we prove a recently proposed conjecture on the equality between E_{F,2}^{G} and the Gaussian intrinsic entanglement. The unified entanglement quantifier emerging from such an equality is then endowed with a direct operational interpretation as the value of a quantum teleportation game.

Oblivious transfer is an important primitive in modern cryptography. Applications include secure multiparty computation, oblivious sampling, e-voting, and signatures. Information-theoretically secure perfect 1-out-of 2 oblivious transfer is impossible to achieve. Imperfect variants, where both participants’ ability to cheat is still limited, are possible using quantum means while remaining classically impossible. Precisely what security parameters are attainable remains unknown. We introduce a theoretical framework for studying semirandom quantum oblivious transfer, which is shown to be equivalent to regular oblivious transfer in terms of cheating probabilities. We then use it to derive bounds on cheating. We also present a protocol with lower cheating probabilities than previous schemes, together with its optical realization. We show that a lower bound of 2/3 on the minimum achievable cheating probability can be directly derived for semirandom protocols using a different method and definition of cheating than used previously. The lower bound increases from 2/3 to approximately 0.749 if the states output by the protocol are pure and symmetric. The oblivious transfer scheme we present uses unambiguous state elimination measurements and can be implemented with the same technological requirements as standard quantum cryptography. In particular, it does not require honest participants to prepare or measure entangled states. The cheating probabilities are 3/4 and approximately 0.729 for sender and receiver, respectively, which is lower than in existing protocols. Using a photonic testbed, we have implemented the protocol with honest parties, as well as optimal cheating strategies. Because of the asymmetry of the receiver’s and sender’s cheating probabilities, the protocol can be combined with a “trivial” protocol to achieve an overall protocol with lower average cheating probabilities of approximately 0.74 for both sender and receiver. This demonstrates that, interestingly, protocols where the final output states are pure and symmetric are not optimal in terms of average cheating probability.