Shannon in celebrated works had shown that n bits of shared key is necessary and sufficient to transmit n-bit classical information in an information-theoretically secure way. Ambainis, Mosca, Tapp and de Wolf in quant-ph/0003101 considered a more general setting, referred to as Private quantum channels, in which instead of classical information, quantum states are required to be transmitted and only one-way communication is allowed. They show that in this case 2n bits of shared key is necessary and sufficient to transmit an n-qubit state. We consider the most general setting in which we allow for all possible combinations i.e. we let the input to be transmitted, the message sent and the shared resources to be classical/quantum. We develop a general framework by which we are able to show tight bounds on communication/shared resources in all of these cases and this includes the results of Shannon and Ambainis et al.
As a consequence of our arguments we also show that in a one-way oblivious Remote state preparation protocol for transferring an n-qubit pure state, the entropy of the communication must be 2n and the entanglement measure of the shared resource must be n. This generalizes on the result of Leung and Shor which shows same bound on the length of communication in the special case when the shared resource is maximally entangled e.g. EPR pairs and hence settles an open question asked in their paper regarding protocols without maximally entangled shared resource.
We consider remote state preparation protocols for a set of pure states whose projectors form a basis for operators acting on the input Hilbert space. If a protocol (1) uses only forward communication and entanglement, (2) deterministically prepares an exact copy of the state, and (3) does so obliviously -- without leaking further information about the state to the receiver -- then the protocol can be modified to require from the sender only a single specimen of the state. Furthermore, the original protocol and the modified protocol use the same amount of classical communication. Thus, under t…
In quantum teleportation, neither Alice nor Bob acquires any classical knowledge on teleported states. The teleportation protocol is said to be oblivious to both parties. In remote state preparation (RSP) it is assumed that Alice is given complete classical knowledge on the state that is to be prepared by Bob. Recently, Leung and Shor showed that the same amount of classical information as that in teleportation needs to be transmitted in any exact and deterministic RSP protocol that is oblivious to Bob. We study similar RSP protocols, but not necessarily oblivious to Bob. First it is shown tha…
A necessary and sufficient condition is given for general exact remote state preparation (RSP) protocols to be oblivious, that is, no information about the target state can be retrieved from the classical message. A novel criterion in terms of commutation relations is also derived for the existence of deterministic exact protocols in which Alice's measurement eigenstates are related to each other by fixed linear operators similar to Bob's unitaries. For non-maximally entangled resources, it provides an easy way to search for RSP protocols. As an example, we show how to reduce the case of parti…
In [ PRL, 102, 010401 (2009)], Spekkens et al., have shown that quantum preparation contextuality can power the parity-oblivious multiplexing (POM) task. The bound on the optimal success probability of $n$-bit POM task performed with the classical resources was shown to be the \textit{same} as in a preparation non-contextual theory. This non-contextual bound is violated if the task is performed with quantum resources. While in $2$-bit POM task the optimal quantum success probability is achieved, in 3-bit case optimality was left as an open question. In this paper, we show that the quantum succ…
The study of ontology (hidden variables) provides for a vital ground on which significant non-classical features of quantum theory are revealed. One such non-classical ontic-feature is preparation contextuality (PC) and advantage in oblivious communication tasks is one of its operational signatures. This article primarily pursues the ontic-feature underlying quantum advantage in communication complexity (CC). We construct oblivious communication tasks tailored to given CC problems. We upper-bound the classical success probability of these oblivious communication tasks, obtaining preparation no…
In a noncontextual hidden variable model of quantum theory, hidden variables determine the outcomes of every measurement in a manner that is independent of how the measurement is implemented. Using a generalization of this notion to arbitrary operational theories and to preparation procedures, we demonstrate that a particular two-party information-processing task, "parity-oblivious multiplexing," is powered by contextuality in the sense that there is a limit to how well any theory described by a noncontextual hidden variable model can perform. This bound constitutes a "noncontextuality inequal…
Higher security and lower failure probability have always been people's pursuits in quantum-oblivious-key-transfer-based private query (QOKT-PQ) protocols since Jacobi \emph{et al}. [Phys. Rev. A 83, 022301 (2011)] proposed the first protocol of this kind. However, higher database security generally has to be obtained at the cost of a higher failure probability, and vice versa. Recently, based on a round-robin differential-phase-shift quantum key distribution protocol, Liu \emph{et al}. [Sci. China-Phys. Mech. Astron.58, 100301 (2015)] presented a private query protocol (RRDPS-PQ protocol) uti…
We provide an interesting two-party parity oblivious communication game whose success probability is solely determined by the Bell expression. The parity-oblivious condition in an operational quantum theory implies the preparation non-contextuality in an ontological model of it. We find that the aforementioned Bell expression has two upper bounds in an ontological model; the usual local bound and a non-trivial preparation non-contextual bound arising from the non-trivial parity-oblivious condition, which is smaller that the local bound. We first demonstrate the communication game when both Ali…
Quantum private query (QPQ) is a kind of quantum protocols to protect both users' privacy in their communication. There is an interesting example, that is, Alice wants to buy one item from Bob's database, which is composed of a quantity of valuable messages. QPQ protocol is the communication procedure ensuring that Alice can get only one item from Bob, and at the same time, Bob cannot know which one was taken by Alice. Owing to its practicability, quantum-key-distribution-based QPQ has draw much attention in recent years. However, the post-processing of the key in such protocols, called oblivi…
Quantum private comparison (QPC) aims to accomplish the equality comparison of the secrets from different users without disclosing their genuine contents by using the principles of quantum mechanics. In this paper, we summarize eight modes of quantum state preparation and transmission existing in current QPC protocols first. Then, by using the mode of scattered preparation and one-way convergent transmission, we construct a new multi-user quantum private comparison (MQPC) protocol with two-particle maximally entangled states, which can accomplish arbitrary pair's comparison of equality among K…
One of the fundamental results in quantum foundations is the Kochen-Specker no-go theorem. For the quantum theory, the no-go theorem excludes the possibility of a class of hidden variable models where value attribution is context independent. Recently, the notion of contextuality has been generalized for different operational procedures and it has been shown that preparation contextuality of mixed quantum states can be a useful resource in an information-processing task called parity-oblivious multiplexing. Here, we introduce a new class of information processing tasks, namely d-level parity o…
In the well-studied cryptographic primitive 1-out-of-N oblivious transfer, a user retrieves a single element from a database of size N without the database learning which element was retrieved. While it has previously been shown that a secure implementation of 1-out-of-N oblivious transfer is impossible against arbitrarily powerful adversaries, recent research has revealed an interesting class of private query protocols based on quantum mechanics in a cheat sensitive model. Specifically, a practical protocol does not need to guarantee that database cannot learn what element was retrieved if do…
We introduce a new multipartite communication scheme, with the aim to enable the senders to remotely and obliviously provide the receivers with an arbitrary amount of multipartite entanglement. The scheme is similar to Remote State Preparation (RSP). However, we show that even though the receivers are restricted to local unitary operations, the required resources for remote entanglement preparation are less than for RSP. In order to do so we introduce a novel canonical form of arbitrary multipartite pure states describing an arbitrary number of qubits. Moreover, we show that if the receivers a…
The optimal success probability of a communication game sets fundamental limitations on an operational theory. Quantum advantage of parity oblivious random access code (PORAC), a communication game, over classical resources reveals the preparation contextuality of quantum theory [Phys. Rev. Lett. 102, 010401 (2009)]. Optimal quantum advantage in the N-dit PORAC game for finite dimensions is an open problem. Here, we show that the degree of uncertainty allowed in an operational theory determines the amount of preparation contextuality. We connect the upper bound of fine-grained uncertainty rela…
We study the cryptographic primitive Oblivious Transfer; a composable construction of this resource would allow arbitrary multi-party computation to be carried out in a secure way, i.e. to compute functions in a distributed way while keeping inputs from different parties private. First we review a framework that allows us to analyze composability of classical and quantum cryptographic protocols in special relativity: Abstract Cryptography implemented with Causal Boxes. We then (1) explore and formalize different versions of oblivious transfer found in the literature, (2) prove that their equiv…
Kochen-Specker (KS) theorem lies at the heart of the foundations of quantum mechanics. It establishes impossibility of explaining predictions of quantum theory by any noncontextual ontological model. Spekkens generalized the notion of KS contextuality in [Phys. Rev. A 71, 052108 (2005)] for arbitrary experimental procedures (preparation, measurement, and transformation procedure). Interestingly, later on it was shown that preparation contextuality powers parity-oblivious multiplexing [Phys. Rev. Lett. 102, 010401 (2009)], a two party information theoretic game. Thus, using resources of a given…
We describe how any two-party quantum computation, specified by a unitary which simultaneously acts on the registers of both parties, can be privately implemented against a quantum version of classical semi-honest adversaries that we call specious. Our construction requires two ideal functionalities to garantee privacy: a private SWAP between registers held by the two parties and a classical private AND-box equivalent to oblivious transfer. If the unitary to be evaluated is in the Clifford group then only one call to SWAP is required for privacy. On the other hand, any unitary not in the Cliff…
Remote state preparation is the variant of quantum state teleportation in which the sender knows the quantum state to be communicated. The original paper introducing teleportation established minimal requirements for classical communication and entanglement but the corresponding limits for remote state preparation have remained unknown until now: previous work has shown, however, that it not only requires less classical communication but also gives rise to a trade-off between these two resources in the appropriate setting. We discuss this problem from first principles, including the various ch…
We introduce a hierarchy of semidefinite relaxations of the set of quantum correlations in generalised contextuality scenarios. This constitutes a simple and versatile tool for bounding the magnitude of quantum contextuality. To illustrate its utility, we use it to determine the maximal quantum violation of several noncontextuality inequalities whose maximum violations were previously unknown. We then go further and use it to prove that certain preparation-contextual correlations cannot be explained with pure states, thereby showing that mixed states are an indispensable resource for contextua…
Although `quantum contextuality' is one of the most fundamental non-classical feature, its generic role in information processing and computation is an open quest. In this article, we present a family of distributed computing tasks pertaining to every logical proof of Kochen-Specker (KS) contextuality in two different one-way communication scenarios: (I) communication of bounded dimensional system, (II) communication of unbounded dimensional system while keeping certain information oblivious, namely, oblivious communication (OC). As the later remains largely unexplored, we introduce a general …
Lucerne School of Computer Science and Information Technology, Lucerne University of Applied Sciences and Arts（卢塞纳应用科学与艺术大学计算机科学与信息技术学院）；Ergon Informatik AG（Ergon信息科技股份公司）
Quantum teleportation uses prior shared entanglement and classical communication to send an unknown quantum state from one party to another. Remote state preparation (RSP) is a similar distributed task in which the sender knows the entire classical description of the state to be sent. (This may also be viewed as the task of non-oblivious compression of a single sample from an ensemble of quantum states.) We study the communication complexity of approximate remote state preparation, in which the goal is to prepare an approximation of the desired quantum state. Jain [Quant. Inf. & Comp., 2006] s…
Device and semi-device independent quantum randomness generators (DI- and SDI-QRNGs) are crucial for applications requiring private randomness. However, they are vulnerable to detection inefficiency attacks and this limits severely their usage for practical purposes. Here, we present a method for protecting SDI-QRNGs in prepare-and-measure scenarios against detection inefficiency attacks. The key idea is the introduction of a blocking device that adds failures in the communication between the preparation and measurement devices. We prove that, for any detection efficiency, there is a blocking …
International Centre for Theory of Quantum Technologies, University of Gdańsk（格但斯克大学量子技术理论国际中心）；Perimeter Institute for Theoretical Physics（基础物理研究所）；Basic Research Community for Physics e.V.（基础物理社区协会）
