In classical two-party computation, a trusted initializer who prepares certain initial correlations, known as one-time tables, can help make the inputs of both parties information-theoretically secure. We propose some bipartite quantum protocols with possible aborts for approximately generating such bipartite classical correlations with varying degrees of privacy, without introducing a third party. Under some weak requirements for the parties, the security level is nontrivial for use in bipartite computation. We show that the security is sometimes dependent on the noise level, but we propose a method for dealing with noise. The security is "forced security", which implies that the probability that some useful one-time tables are generated can approach $1$ in the noiseless case under quite weak assumptions about the parties, although the protocols allow aborts. We show how to use the generated one-time tables to achieve nontrivial information-theoretic security in generic two-party classical or quantum computation tasks, including (interactive) quantum homomorphic encryption. Our methods provide check-based implementations of some no-signaling correlations, including the PR-box type, with the help of communication which carry no information about the inputs in the generated correlations.
We propose three constructions of classically verifiable non-interactive zero-knowledge proofs and arguments (CV-NIZK) for QMA in various preprocessing models. - We construct a CV-NIZK for QMA in the quantum secret parameter model where a trusted setup sends a quantum proving key to the prover and a classical verification key to the verifier. It is information theoretically sound and zero-knowledge. - Assuming the quantum hardness of the learning with errors problem, we construct a CV-NIZK for QMA in a model where a trusted party generates a CRS and the verifier sends an instance-independent q…
We investigate definitions of and protocols for multi-party quantum computing in the scenario where the secret data are quantum systems. We work in the quantum information-theoretic model, where no assumptions are made on the computational power of the adversary. For the slightly weaker task of verifiable quantum secret sharing, we give a protocol which tolerates any t < n/4 cheating parties (out of n). This is shown to be optimal. We use this new tool to establish that any multi-party quantum computation can be securely performed as long as the number of dishonest players is less than n/6.
Duan, Giedke, Cirac and Zoller (quant-ph/9908056) and, independently, Simon (quant-ph/9909044) have recently found necessary and sufficient conditions for the separability (classical correlation) of the Gaussian two-party (continuous variable) states. Duan et al remark that their criterion is based on a "much stronger bound" on the total variance of a pair of Einstein-Podolsky-Rosen-type operators than is required simply by the uncertainty relation. Here, we seek to formalize and test this particular assertion in both classical and quantum-theoretic frameworks. We first attach to these states …
Secure multi-party computing, also called "secure function evaluation", has been extensively studied in classical cryptography. We consider the extension of this task to computation with quantum inputs and circuits. Our protocols are information-theoretically secure, i.e. no assumptions are made on the computational power of the adversary. For the weaker task of verifiable quantum secret sharing, we give a protocol which tolerates any t < n/4 cheating parties (out of n). This is shown to be optimal. We use this new tool to show how to perform any multi-party quantum computation as long as the …
In the last few years, there has been a great interest in extending the information-theoretic scenario for the non-asymptotic or one-shot case, i.e., where the channel is used only once. We provide the one-shot rate region for the distributed source-coding (Slepian-Wolf) and the multiple-access channel. Our results are based on defining a novel one-shot typical set based on smooth entropies that yields the one-shot achievable rate regions while leveraging the results from the asymptotic analysis. Our results are asymptotically optimal, i.e., for the distributed source coding they yield the sam…
We give a proof of the multi-party typicality conjecture for the first nontrivial case when there are only two parties. The conjecture itself is motivated by the study of multi-party state merging protocols on quantum systems. Our approach is based on fundamental group-theoretical properties, thereby providing an opportunity to study the problem from a more systematic perspective. Our proof also covers an extended multiparty typicality conjecture that we state in this work. This extended multiparty typicality conjecture is formulated using arbitrary $k$-norms instead of only the $2$-norm as in…
We study the classical and quantum values of one- and two-party linear games, an important class of unique games that generalizes the well-known XOR games to the case of non-binary outcomes. We introduce a ``constraint graph" associated to such a game, with the constraints defining the linear game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation …
The quantum key distribution network with Vernam's One Time Pad encryption and secret sharing are powerful security tools to realize an information theoretically secure distributed storage system. In our previous work, a single-password-authenticated secret sharing scheme based on the QKD network and Shamir's secret sharing was experimentally demonstrated; it confirmed ITS data transmission, storage, authentication, and integrity. To achieve data integrity, an ITS message authentication code tag is employed and a data owner of the secret sharing performs both the MAC tag generation and verific…
Quantum Advantage for Two-Party Differential Privacy
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机科学联合中心，美国国家标准与技术研究院/马里兰大学）；Joint Quantum Institute, NIST/University of Maryland（量子研究所，美国国家标准与技术研究院/马里兰大学）
The characterization of the set of quantum correlations is a problem of fundamental importance in quantum information. The question whether every proper (tight) Bell inequality is violated in Quantum theory is an intriguing one in this regard. Here, we make significant progress in answering this question, by showing that every tight Bell inequality is violated by 'Almost Quantum' correlations, a semi-definite programming relaxation of the set of quantum correlations. As a consequence, we show that many (classes of) Bell inequalities including two-party correlation Bell inequalities and multi-o…
One-time tables are a class of two-party correlations that can help achieve information-theoretically secure two-party (interactive) classical or quantum computation. In this work we propose a bipartite quantum protocol for generating a simple type of one-time tables (the correlation in the Popescu-Rohrlich nonlocal box) with partial security. We then show that by running many instances of the first protocol and performing checks on some of them, asymptotically information-theoretically secure generation of one-time tables can be achieved. The first protocol is adapted from a protocol for semi…
Let $|Ψ>$ be an arbitrary stabilizer state distributed between three remote parties, such that each party holds several qubits. Let $S$ be a stabilizer group of $|Ψ>$. We show that $|Ψ>$ can be converted by local unitaries into a collection of singlets, GHZ states, and local one-qubit states. The numbers of singlets and GHZs are determined by dimensions of certain subgroups of $S$. For an arbitrary number of parties $m$ we find a formula for the maximal number of $m$-partite GHZ states that can be extracted from $|Ψ>$ by local unitaries. A connection with earlier introduced measures of multipa…
Einstein-Podolsky-Rosen steering refers to the quantum phenomenon whereby the state of a system held by one party can be "steered" into different states at the will of another, distant, party by performing different local measurements. Although steering has been demonstrated in a number of experiments involving qubits, the question of which two-qubit states are steerable remains an open theoretical problem. Here, we derive a necessary condition for any two-qubit state to be steerable when the steering party suffers from a given probability of qubit loss. Our main result finds application in on…
Quantum homomorphic encryption (QHE) is an encryption method that allows quantum computation to be performed on one party's private data with the program provided by another party, without revealing much information about the data nor about the program to the opposite party. It is known that information-theoretically-secure QHE for circuits of unrestricted size would require exponential resources, and efficient computationally-secure QHE schemes for polynomial-sized quantum circuits have been constructed. In this paper we first propose a QHE scheme for a type of circuits of polynomial depth, b…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of distributed quantum systems that play a significant role in quantum error correction, multi-party quantum communication, and quantum computation within the framework of the one-way quantum computer. We characterize and quantify the genuine multi-particle entanglement of such graph states in terms of the Schmidt measure, to which we provide upper and lower bounds in…
Central cryptographic functionalities such as encryption, authentication, or secure two-party computation cannot be realized in an information-theoretically secure way from scratch. This serves as a motivation to study what (possibly weak) primitives they can be based on. We consider as such starting points general two-party input-output systems that do not allow for message transmission, and show that they can be used for realizing unconditionally secure bit commitment as soon as they are non-trivial, i.e., cannot be securely realized from distributed randomness only.
Quantum digital signatures (QDSs) promise information-theoretic security against repudiation and forgery of messages. Compared with currently existing three-party QDS protocols, multiparty protocols have unique advantages in the practical case of more than two receivers when sending a mass message. However, complex security analysis, numerous quantum channels and low data utilization efficiency make it intractable to expand three-party to multiparty scenario. Here, based on six-state non-orthogonal encoding protocol, we propose an effective multiparty QDS framework to overcome these difficulti…
Quantum steering, loosely speaking the distribution of entanglement from an untrusted party, is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. Determining which states can be steered is important from a conceptual point of view, but also for applications, e.g. in quantum cryptography. Here we show that bound entanglement, although it represents the weakest form of entanglement, can nevertheless lead to quantum steering. This is done by noticing that steering inequalities can be derived from entropic uncertainty relations. Our result has implicati…
Bit commitment is a fundamental cryptographic primitive in which a party wishes to commit a secret bit to another party. Perfect security between mistrustful parties is unfortunately impossible to achieve through the asynchronous exchange of classical and quantum messages. Perfect security can nonetheless be achieved if each party splits into two agents exchanging classical information at times and locations satisfying strict relativistic constraints. A relativistic multi-round protocol to achieve this was previously proposed and used to implement a 2~millisecond commitment time. Much longer d…
We consider the task of distilling local purity from a noisy quantum state $ρ^{ABC}$, wherein we provide a protocol for three parties, Alice, Bob and Charlie, to distill local purity (at a rate $P$) from many independent copies of a given quantum state $ρ^{ABC}$. The three parties have access to their respective subsystems of $ρ^{ABC}$, and are provided with pure ancilla catalytically, i.e., with the promise of returning them unaltered after the end of the protocol. In addition, Alice and Bob can communicate with Charlie using a one-way multiple-access dephasing channel of link rates $R_1$ and…
Unlike classical correlation, quantum entanglement cannot be freely shared among many parties. This restricted shareability of entanglement among multi-party systems is known as monogamy of entanglement, which is one of the most fundamental properties of entanglement. Here, we summarize recent theoretical progress in the field of monogamy of entanglement. We firstly review the standard CKW-type monogamy inequalities in terms of various entanglement measures. In particular, the squashed entanglement and one-way distillable entanglement are monogamous for arbitrary dimensional systems. We then i…
Einstein-Rosen-Podolsky (EPR) steering or quantum steering describes the "spooky-action-at-a-distance" that one party is able to remotely alter the states of the other if they share a certain entangled state. Generally, it admits an operational interpretation as the task of verifying entanglement without trust in the steering party's devices, making it lying intermediate between Bell nonlocality and entanglement. Together with the asymmetrical nature, quantum steering has attracted a considerable interest from theoretical and experimental sides over past decades. In this Perspective, we presen…
Quantum communication has been leading the way of many remarkable theoretical results and experimental tests in physics. In this context, quantum communication complexity (QCC) has recently drawn earnest research attention as a tool to optimize the amounts of transmitted qubits and energy that are required to implement distributed computational tasks. On this matter, we introduce a novel multi-user quantum fingerprinting protocol that is ready to be implemented with existing technology. Particularly, we extend to the multi-user framework a well-known two-user coherent-state fingerprinting sche…
For distinguishing quantum states sampled from a fixed ensemble, the gap in bipartite and single-party distinguishability can be interpreted as a nonlocality of the ensemble. In this paper, we consider bipartite state discrimination in a composite system consisting of $N$ subsystems, where each subsystem is shared between two parties and the state of each subsystem is randomly sampled from a particular ensemble comprising the Bell states. We show that the success probability of perfectly identifying the state converges to $1$ as $N\rightarrow\infty$ if the entropy of the probability distributi…
In the context of holographic duality with AdS3 asymptotics, the Ryu-Takayanagi formula states that the entanglement entropy of a subregion is given by the length of a certain bulk geodesic. The entanglement entropy can be operationalized as the entanglement cost necessary to transmit the state of the subregion from one party to another while preserving all correlations with a reference party. The question then arises as to whether the lengths of other bulk curves can be interpreted as entanglement costs for some other information theoretic tasks. Building on recent results showing that the le…
We show that superselection rules do not enhance the information-theoretic security of quantum cryptographic protocols. Our analysis employs two quite different methods. The first method uses the concept of a reference system -- in a world subject to a superselection rule, unrestricted operations can be simulated by parties who share access to a reference system with suitable properties. By this method, we prove that if an n-party protocol is secure in a world subject to a superselection rule, then the security is maintained even if the superselection rule is relaxed. However, the proof applie…
