Quantum Private Comparison: A Review

As an important branch of quantum secure multiparty computation, quantum private comparison (QPC) has attracted more and more attention recently. In this paper, according to the quantum implementation mechanism that these protocols used, we divide these protocols into three categories: The quantum cryptography QPC, the superdense coding QPC, and the entanglement swapping QPC. And then, a more in-depth analysis on the research progress, design idea, and substantive characteristics of corresponding QPC categories is carried out, respectively. Finally, the applications of QPC and quantum secure multi-party computation issues are discussed and, in addition, three possible research mainstream directions are pointed out

Quantum cryptography: key distribution and beyond

Uniquely among the sciences, quantum cryptography has driven both foundational research as well as practical real-life applications. We review the progress of quantum cryptography in the last decade, covering quantum key distribution and other applications.Comment: It's a review on quantum cryptography and it is not restricted to QK

Multi-party quantum private comparison of size relationship with two third parties based on d-dimensional Bell states

In this paper, we put forward a multi-party quantum private comparison (MQPC) protocol with two semi-honest third parties (TPs) by adopting d-dimensional Bell states, which can judge the size relationship of private integers from more than two users within one execution of protocol. Each TP is permitted to misbehave on her own but cannot collude with others. In the proposed MQPC protocol, TPs are only required to apply d-dimensional single-particle measurements rather than d-dimensional Bell state measurements. There are no quantum entanglement swapping and unitary operations required in the proposed MQPC protocol. The security analysis validates that the proposed MQPC protocol can resist both the outside attacks and the participant attacks. The proposed MQPC protocol is adaptive for the case that users want to compare the size relationship of their private integers under the control of two supervisors. Furthermore, the proposed MQPC protocol can be used in the strange user environment, because there are not any communication and pre-shared key between each pair of users.Comment: 15 pages, 1 figure, 1 tabl

Energy-constrained two-way assisted private and quantum capacities of quantum channels

With the rapid growth of quantum technologies, knowing the fundamental characteristics of quantum systems and protocols is essential for their effective implementation. A particular communication setting that has received increased focus is related to quantum key distribution and distributed quantum computation. In this setting, a quantum channel connects a sender to a receiver, and their goal is to distill either a secret key or entanglement, along with the help of arbitrary local operations and classical communication (LOCC). In this work, we establish a general theory of energy-constrained, LOCC-assisted private and quantum capacities of quantum channels, which are the maximum rates at which an LOCC-assisted quantum channel can reliably establish secret key or entanglement, respectively, subject to an energy constraint on the channel input states. We prove that the energy-constrained squashed entanglement of a channel is an upper bound on these capacities. We also explicitly prove that a thermal state maximizes a relaxation of the squashed entanglement of all phase-insensitive, single-mode input bosonic Gaussian channels, generalizing results from prior work. After doing so, we prove that a variation of the method introduced in [Goodenough et al., New J. Phys. 18, 063005 (2016)] leads to improved upper bounds on the energy-constrained secret-key-agreement capacity of a bosonic thermal channel. We then consider a multipartite setting and prove that two known multipartite generalizations of the squashed entanglement are in fact equal. We finally show that the energy-constrained, multipartite squashed entanglement plays a role in bounding the energy-constrained LOCC-assisted private and quantum capacity regions of quantum broadcast channels.Comment: 31 pages, 6 figure

Quantum information with continuous variables

Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement. We review the progress in quantum information based on continuous quantum variables, with emphasis on quantum optical implementations in terms of the quadrature amplitudes of the electromagnetic field.Comment: accepted for publication in Reviews of Modern Physic

Reference frames, superselection rules, and quantum information

Recently, there has been much interest in a new kind of ``unspeakable'' quantum information that stands to regular quantum information in the same way that a direction in space or a moment in time stands to a classical bit string: the former can only be encoded using particular degrees of freedom while the latter are indifferent to the physical nature of the information carriers. The problem of correlating distant reference frames, of which aligning Cartesian axes and synchronizing clocks are important instances, is an example of a task that requires the exchange of unspeakable information and for which it is interesting to determine the fundamental quantum limit of efficiency. There have also been many investigations into the information theory that is appropriate for parties that lack reference frames or that lack correlation between their reference frames, restrictions that result in global and local superselection rules. In the presence of these, quantum unspeakable information becomes a new kind of resource that can be manipulated, depleted, quantified, etcetera. Methods have also been developed to contend with these restrictions using relational encodings, particularly in the context of computation, cryptography, communication, and the manipulation of entanglement. This article reviews the role of reference frames and superselection rules in the theory of quantum information processing.Comment: 55 pages, published versio

A novel multi-party semiquantum private comparison protocol of size relationship with d-dimensional single-particle states

By using d-level single-particle states, the first multi-party semiquantum private comparison (MSQPC) protocol which can judge the size relationship of private inputs from more than two classical users within one execution of protocol is put forward. This protocol requires the help of one quantum third party (TP) and one classical TP, both of whom are allowed to misbehave on their own but cannot conspire with anyone else. Neither quantum entanglement swapping nor unitary operations are necessary for implementing this protocol. TPs are only required to perform d-dimensional single-particle measurements. The correctness analysis validates the accuracy of the compared results. The security analysis verifies that both the outside attacks and the participant attacks can be resisted.Comment: 19 pages, 2 figures, 2 table

Entanglement Verification in Quantum Networks with Tampered Nodes

In this paper, we consider the problem of entanglement verification across the quantum memories of any two nodes of a quantum network. Its solution can be a means for detecting (albeit not preventing) the presence of intruders that have taken full control of a node, either to make a denial-of-service attack or to reprogram the node. Looking for strategies that only require local operations and classical communication (LOCC), we propose two entanglement verification protocols characterized by increasing robustness and efficiency.Comment: 14 pages, 7 figure