Search

Discriminative Canonical Correlation Analysis (DCCA) is a powerful supervised feature extraction technique for two sets of multivariate data, which has wide applications in pattern recognition. DCCA consists of two parts: (i) mean-centering that subtracts the sample mean from the sample; (ii) solving the generalized eigenvalue problem. The cost of DCCA is expensive when dealing with a large number of high-dimensional samples. To solve this problem, here we propose a quantum DCCA algorithm. Specifically, we devise an efficient method to compute the mean of all samples, then use block-Hamiltonian simulation and quantum phase estimation to solve the generalized eigenvalue problem. Our algorithm achieves a polynomial speedup in the dimension of samples under certain conditions over its classical counterpart.

Self-testing refers to a device-independent way to uniquely identify an unknown quantum device based only on the observed statistics. Earlier results on self-testing of multipartite state were restricted either to Dicke states or Graph states. In this paper, we propose self-testing schemes for a large family of symmetric three-qubit states, namely the superposition of $W$ state and $GHZ$ state. We first propose and analytically prove a self-testing criterion for the special symmetric state with equal coefficients of the canonical bases, by designing subsystem self-testing of partially and maximally entangled state simultaneously. Then we demonstrate for the general case, the states can be self-tested numerically by the swap method combining semidefinite programming (SDP) in high precision.

Most existing quantum private query (QPQ) protocols can hardly work in the presence of noise. The user Alice may obtain a false database item in noisy environments and both participants may cheat under the disguise of noise, so dealing with the noise needs an overall consideration of error correction, user privacy and database security. However, the only two existing protocols aiming to correct errors in QPQ lack such an overall consideration (at least one party’s privacy can be revealed), and they did not estimate what extent of errors can be tolerated (actually, noise is seldom discussed in quantum two-party secure computations, and to the best of our knowledge, relevant bounds on tolerable errors remain unattainable so far). To solve this problem, we first exemplify how one participant reveals the other party’s privacy in the existing QPQ protocols aiming to correct errors. Then we propose a practical protocol which can really work via noisy channel, that is, the error rate of the retrieved database item is reduced significantly and both parties’ privacy are well protected. Besides, we deduce that the final error rate, user privacy and database security are pairwise in a “trade-off” relationship. By balancing them according to the required level of security and reliability, we obtain an upper bound on tolerable errors.

The non-classical correlations presented in quantum random access code experiment are a powerful diagnostic tool for semi-device-independent random number generator protocols. The idea behind it is that if the user observes the optimal non-classical correlations, he has the guarantee that the unknown quantum states and measurements in the devices have carefully calibrated (we say have global reference frame), in a relationship which can bring to random outcomes. This means, for observing the non-classical correlations, the devices must have that calibration in previous. However, that calibration can’t always be guaranteed in reality due to unintentional flaws or failures of the quantum apparatuses, thus the devices do not always occur the wanted non-classical correlations. In this paper, we show there will always have non-classical correlations by the proper operations, when the devices have local reference. The quantity of true randomness in the observed non-classical correlations is then quantified by the violation values of some inequality. Besides we also consider the devices without local reference and show the probability of non-classical correlations occurring in 100 trials.

In this paper, we mainly study the local distinguishability of mutually orthogonal maximally entangled states in canonical form. In $$d \otimes d$$d?d, Nathanson (Phys Rev A 88:062316, 2013) presented a feasible necessary and sufficient condition for distinguishing the general bipartite quantum states by one-way local operations and classical communication (LOCC). However, for maximally entangled states in canonical form, it is still unknown how to more effectively judge whether there exists a state such that those unitary operators corresponding to those maximally entangled states are pairwise orthogonal. In this work, we exhibit one method which can be used to more effectively judge it. Furthermore, we construct some sets of maximally entangled states and can easily know that those states are not distinguished by one-way LOCC with the help of our new method.

In order to realize long-distance and large-scale quantum communication, it is natural to utilize quantum repeater. For a general quantum multiple-unicast network, it is still puzzling how to complete communication tasks perfectly with less resources such as registers. In this paper, we solve this problem. By applying quantum repeaters to multiple-unicast communication problem, we give encoding---decoding schemes for source nodes, internal ones and target ones, respectively. Source-target nodes share EPR pairs by using our encoding---decoding schemes over quantum multiple-unicast network. Furthermore, quantum communication can be accomplished perfectly via teleportation. Compared with existed schemes, our schemes can reduce resource consumption and realize long-distance transmission of quantum information.

So far, very little is known about local indistinguishability of multipartite orthogonal product bases except some special cases. We first give a method to construct an orthogonal product basis with n parties each holding a $$\frac{1}{2}(n+1)$$ -dimensional system, where $$n\ge 5$$ and n is odd. The proof of the local indistinguishability of the basis exhibits that it is a sufficient condition for the local indistinguishability of an orthogonal multipartite product basis that all the positive operator-valued measure elements of each party can only be proportional to the identity operator to make further discrimination feasible. Then, we construct a set of n-partite product states, which contains only 2n members and cannot be perfectly distinguished by local operations and classic communication. All the results lead to a better understanding of the phenomenon of quantum nonlocality without entanglement in multipartite and high-dimensional quantum systems.

In many circumstances, a shared key is needed to realize secure communication. Based on quantum mechanics principles, quantum key agreement (QKA) is a good method to establish a shared key by every party's fair participation. In this paper, we propose a novel three-party QKA protocol, which is designed by using Greenberger---Horne---Zeilinger (GHZ) states. To realize the protocol, the distributor of the GHZ states needs only one quantum communication with the other two parties, respectively, and everyone performs single-particle measurements simply. Then, we extend the three-party QKA protocol to arbitrary multiparty situation. At last, we discuss the security and fairness of the multiparty protocol. It shows that the new scheme is secure and fair to every participant.

Existing arbitrated quantum signature (AQS) schemes are almost all based on the Leung quantum one-time pad (L-QOTP) algorithm. In these schemes, the receiver can achieve an existential forgery of the sender's signatures under the known message attack, and the sender can successfully disavow any of her/his signatures by a simple attack. In this paper, a solution of solving the problems is given, through designing a new QOTP algorithm relying largely on inserting decoy states into fixed insertion positions. Furthermore, we present an AQS scheme with fast signing and verifying, which is based on the new QOTP algorithm. It is just using single particle states and is unconditional secure. To fulfill the functions of AQS schemes, our scheme needs a significantly lower computational costs than that required by other AQS schemes based on the L-QOTP algorithm.

The general theory of three-party QSS protocols with the noisy quantum channels is discussed. When the particles are transmitted through the noisy quantum channels, the initial pure three-qubit tripartite entangled states would be changed into mixed states. We analyze the security of QSS protocols with the different kinds of three-qubit tripartite entangled states under phase-damping channels and figure out, for different kinds of initial states, the successful probabilities that Alice's secret can be recovered by legal agents are different. Comparing with one recent QSS protocol based on GHZ states, our scheme is secure, and has a little smaller key rate than that of the recent protocol.

Cheat sensitive quantum bit commitment is a most important and realizable quantum bit commitment (QBC) protocol. By taking advantage of quantum mechanism, it can achieve higher security than classical bit commitment. In this paper, we propose a QBC schemes based on pre- and post-selected quantum states. The analysis indicates that both of the two participants' cheat strategies will be detected with non-zero probability. And the protocol can be implemented with today's technology as a long-term quantum memory is not needed.

In this paper, we propose a quantum private comparison protocol based on entanglement swapping, where two distrustful parties can compare the values of their secrets with the help of a semi-trusted third party. The protocol can determine not only whether two secrets are equal, but also the size relationship between them. The two parties can deduce the comparison result based on the keys shared between them and the announcement of the third party. Others including the third party will learn nothing about the values of the secrets, as well as the comparison result. The security of our protocol is analyzed. Furthermore, all the particles can be reused in the same protocol model theoretically. So our protocol is efficient and feasible to expand in network service, which in turn gives a solution to the left problem in Lin et al. (Quantum Inf Process, doi: 10.1007/s11128-012-0395-6 , 2012).

In this paper, we propose a practical quantum all-or-nothing oblivious transfer protocol. Its security is based on technological limitations on non-demolition measurements and long-term quantum memory, and it has the capabilities of loss-tolerance and error-correction.

In this paper, we propose a quantum private comparison scheme which can be used in decoherence noise scenario. With the combination of decoherence-free states and error-correcting code, it achieves a fault tolerant quantum private comparison to prevent collective decoherence noise and limited other decoherence noise. And the third party used in the protocol is not needed to be semi-honest.

Cryptanalysis is an important branch in the study of cryptography, including both the classical cryptography and the quantum one. In this paper we analyze the security of two three-party quantum key distribution protocols (QKDPs) proposed recently, and point out that they are susceptible to a simple and effective attack, i.e. the dense-coding attack. It is shown that the eavesdropper Eve can totally obtain the session key by sending entangled qubits as the fake signal to Alice and performing collective measurements after Alice's encoding. The attack process is just like a dense-coding communication between Eve and Alice, where a special measurement basis is employed. Furthermore, this attack does not introduce any errors to the transmitted information and consequently will not be discovered by Alice and Bob. The attack strategy is described in detail and a proof for its correctness is given. At last, the root of this insecurity and a possible way to improve these protocols are discussed., 6 pages, 3 figures

We analyze the security of multiparty controlled quantum secure direct communication using Greenberger–Horne–Zeilinger (GHZ) state. It is shown that the receiver, using a special property of GHZ state, can illegally obtain 33.3% of the sender’s secret without any controller’s permission. The attack strategy is demonstrated in detail and an improvement of this protocol is discussed. The idea of this attack might be instructive for the cryptanalysis of quantum cryptographic protocols.

A scalable protocol for multiparty quantum secret splitting with collective eavesdropping-check is proposed by using Einstein–Podolsky–Rosen pairs. We analyze the security of this protocol and prove that it can stand against some possible attacks in an ideal condition. Meanwhile, this protocol utilizes quantum dense coding to achieve a high intrinsic efficiency and source capacity. Moreover, only Bell-state measurement and local unitary operations are required, which makes this protocol more convenient from an applied point of view.

The security of quantum secure direct communication by entangled qutrits and entanglement swapping [Y.B. Zhan et al., Opt. Commun. 282 (2009) 4633] is analyzed. It is shown that an eavesdropper can obtain all the secret without being found by a simple intercept-and-resend attack. Finally, a possible improvement to resist this attack is proposed.

The security of a secure quantum sealed-bid auction protocol using quantum secure direct communication [Mosayeb Naseri, Opt. Commun. 282 (2009) 1939] is analyzed. It is shown that this protocol is unfair as a malicious bidder can obtain others’ bids without being found, and then he can optimize his bid to win the auction. Finally, a simple improvement to resist this attack is proposed.

The security of a deterministic secure quantum communication using four-particle genuine entangled state and entanglement swapping [X.M. Xiu, H.K. Dong, L. Dong, Y.J. Cao, F. Chi, Opt. Commun. 282 (2009) 2457] is analyzed. It is shown that an eavesdropper can entangle an ancilla without introducing any error in the security test utilizing a speciality of the four-particle genuine entangled state. Moreover, the eavesdropper can distill a quarter of the secret information from her entangled ancilla. Finally, a simple improvement to resist this attack is proposed.

A controlled deterministic secure quantum communication protocol [X.M. Xiu, L. Dong, Y.J. Cao, F. Chi, Opt. Commun. 282 (2009) 333] with five-qubit entangled states was proposed recently. The aim of Xiu et al. was that the successful realization of communication between Alice and Bob needed the cooperation of a controller, Charlie. However, we show that the controller Charlie’s role could be excluded unknowingly. Moreover, an eavesdropper can entangle an ancilla without introducing any error in the first security test and then she can distill a quarter of the secret messages from her entangled ancilla.

The security of a multiparty quantum secret sharing protocol [L.F. Han, Y.M. Liu, J. Liu, Z.J. Zhang, Opt. Commun. 281 (2008) 2690] is reexamined. It is shown that any one dishonest participant can obtain all the transmitted secret bits by a special attack, where the controlled- ( - i σ y ) gate is employed to invalidate the role of the random phase shift operation. Furthermore, a possible way to resist this attack is discussed.