The entropy of a quantum system is a measure of its randomness, and has applications in measuring quantum entanglement. We study the problem of estimating the von Neumann entropy, S(), and R矇nyi entropy, S帢() of an unknown mixed quantum state in d dimensions, given access to independent copies of . We provide algorithms with copy complexity O(d2/帢) for estimating S帢() for 帢 <; 1, and copy complexity O(d2) for estimating S(), and S帢() for non-integral 帢 > 1.
In the classical private information retrieval (PIR) setup, a user wants to retrieve a file from a database or a distributed storage system (DSS) without revealing the file identity to the servers holding the data. In the quantum PIR (QPIR) setting, a user privately retrieves a classical file by receiving quantum information from the servers. The QPIR problem has been treated by Song et al. in the case of replicated servers, both without collusion and with all but one servers colluding.
A common scenario in distributed computing involves a client who asks a server to perform a computation on a remote computer. An important problem is to determine the minimum amount of communication needed to specify the desired computation. Here we extend this problem to the quantum domain, analyzing the total amount of (classical and quantum) communication needed by a server in order to accurately execute a quantum process chosen by a client from a parametric family of quantum processes.
Due to Csisz獺r and K繹rner, the private capacity of classical wiretap channels has a single-letter characterization in terms of the private information. For quantum wiretap channels, however, it is known that regularization of the private information is necessary to reach the capacity. Here, we study hybrid classical-quantum wiretap channels in order to resolve to what extent quantum effects are needed to witness non-additivity phenomena in quantum Shannon theory.
We introduce a new setting for two-party cryptography by introducing the notion of temporarily trusted third parties. These third parties act honest-but-curious during the execution of the protocol. Once the protocol concludes and the trust period expires, these third parties may collaborate with an adversarial party. We implement a variant of the cryptographic primitive of bit commitment in this setting, which we call erasable bit commitment. In this primitive, the sender has the choice of either opening or erasing her commitment after the commit phase.
We propose a protocol based on pulse-position modulation and multi-level coding that allows one to bootstrap traditional quantum key distribution protocols while ensuring covertness, in the sense that no statistical test by the adversary can detect the presence of communication over the quantum channel better than a random guess. When run over a bosonic channel, our protocol can leverage existing discrete-modulated continuous-variable protocols.
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit-measures of statistical distance-and demonstrate the crucial differences which arise in the quantum regime in contrast to the classical setting.
Recently, Anshu et al. introduced partially smoothed information measures and used them to derive tighter bounds for several information-processing tasks, including quantum state merging and privacy amplification against quantum adversaries [91勛圖厙 Trans. Inf. Theory 66, 5022 (2020)]. Yet, a tight second-order asymptotic expansion of the partially smoothed conditional min-entropy in the i.i.d. setting remains an open question.
We introduce and analyse a multiple-access channel with two senders and one receiver, in the presence of i.i.d. noise coming from the environment. Partial side information about the environmental states allows the senders to modulate their signals accordingly. An adversarial jammer with its own access to information on environmental states and the modulation signals can jam a fraction of the transmissions.
It is known that quantum resources can allow us to achieve a family of equilibria that can have sometimes a better social welfare, while guaranteeing privacy. We use graph games to propose a way to build non-cooperative games from graph states, and we show how to achieve an unlimited improvement with quantum advice compared to classical advice.