Two-party Quantum Research Articles

Two-party quantum key agreement based on four-particle GHZ states

Based on four-particle GHZ states, the double CNOT operation and the delayed measurement technique, a two-party quantum key agreement (QKA) protocols is proposed. The double CNOT operation makes each four-particle GHZ state collapse into two independent quantum states without any entanglement. Furthermore, one party can directly know the two quantum states and the other party can be aware of the two quantum states by using the corresponding measurement. According to the initial states of the two quantum states, two parties can extract the secret keys of each other by using the publicly announced value or by performing the delayed measurement, respectively. Then the protocol achieves the fair establishment of a shared key. The security analysis shows that the new protocol can resist against participant attacks, the Trojan horse attacks and other outsider attacks. Furthermore, the new protocol also has no information leakage problem and has high qubit efficiency.

State Ensembles and Quantum Entropy

This paper considers quantum communication involving an ensemble of states. Apart from the von Neumann entropy, it considers other measures one of which may be useful in obtaining information about an unknown pure state and another that may be useful in quantum games. It is shown that under certain conditions in a two-party quantum game, the receiver of the states can increase the entropy by adding another pure state.

Controlling the key by choosing the detection bits in quantum cryptographic protocols

Eavesdropping detection is an indispensable process of most quantum cryptographic protocols. By publishing and comparing part of the shared bits, called as detection bits, the participants can check whether there exists an eavesdropper. Generally, the detection bits are chosen randomly. Consequently, the secret bits, i.e., the rest bits, are also random. Then, what if the detection bits are chosen non-randomly? Can the participant who chooses the detection bits make the secret bits to be a predetermined string he expected? This paper focuses on the participants’ key control capability when they choose the detection bits selectively in two-party quantum communication protocols. Concretely, we analyze the participants’ key control capability in different situations of different proportions of the detection bits. And we prove that the participants can predetermine, with high probability, any part of the secret bits of which the length is smaller than that of the detection bits. The above result has various potential applications in quantum cryptographic protocols. Obviously, utilizing this non-random selection of the detection bits, one can realize the function of a deterministic quantum key distribution protocol through a random one if the number of the detection bits is not smaller than that of the secret bits. What is more, we find that quite a few quantum key agreement protocols cannot guarantee the fairness of the key in the sense that the participant who chooses the detection bits can control the key somewhat.

Twice-Hadamard-CNOT attack on Li et al.’s fault-tolerant quantum private comparison and the improved scheme

Recently, Li et al. presented a two-party quantum private comparison scheme using Greenberger-Horne-Zeilinger (GHZ) states and error-correcting code (ECC) [Int. J. Theor. Phys. 52, 2818 (2013)], claiming it is fault-tolerant and could be performed in a non-ideal scenario. However, there exists a fatal loophole in their private comparison scheme under a special attack, namely the twice-Hadamard-CNOT attack. Specifically, a malicious party may intercept the other party’s particles and execute Hadamard operations on the intercepted particles as well as on his or her own particles. Then, the malicious party could sequentially perform a controlled-NOT (CNOT) operation between intercepted particles and the auxiliary particles, as well as between his or her own particles and the auxiliary particles prepared in advance. By measuring the auxiliary particles, the secret input will be revealed to the malicious party without being detected. For resisting this special attack, a feasible improved scheme is proposed by introducing a permutation operator before the third party (TP) sends the particle sequences to each participant.

Communication complexity and the reality of the wave function

In this review, we discuss a relation between quantum communication complexity and a long-standing debate in quantum foundation concerning the interpretation of the quantum state. Is the quantum state a physical element of reality as originally interpreted by Schrödinger? Or is it an abstract mathematical object containing statistical information about the outcome of measurements as interpreted by Born? Although these questions sound philosophical and pointless, they can be made precise in the framework of what we call classical theories of quantum processes, which are a reword of quantum phenomena in the language of classical probability theory. In 2012, Pusey, Barrett and Rudolph (PBR) proved, under an assumption of preparation independence, a theorem supporting the original interpretation of Schrödinger in the classical framework. The PBR theorem has attracted considerable interest revitalizing the debate and motivating other proofs with alternative hypotheses. Recently, we showed that these questions are related to a practical problem in quantum communication complexity, namely, quantifying the minimal amount of classical communication required in the classical simulation of a two-party quantum communication process. In particular, we argued that the statement of the PBR theorem can be proved if the classical communication cost of simulating the communication of n qubits grows more than exponentially in n. Our argument is based on an assumption that we call probability equipartition property. This property is somehow weaker than the preparation independence property used in the PBR theorem, as the former can be justified by the latter and the asymptotic equipartition property of independent stochastic sources. The probability equipartition property is a general and natural hypothesis that can be assumed even if the preparation independence hypothesis is dropped. In this review, we further develop our argument into the form of a theorem.

Secure quantum private query with real-time security check

Secure quantum private query with real-time security check

Two-party quantum key agreement with four-qubit cluster states

Based on four-qubit cluster states, we present a two-party quantum key agreement (QKA) scheme using unitary operations. In this scheme, two participants perform the unitary operation on the different photon of the same cluster state, which guarantees that each party contributes equally to the agreement key. By measuring each cluster state and decoding, these two participants can generate a four-bit classical key without the exchange of classical bits between them. Compared with other existed two-party QKA protocols, our scheme is efficient. Security analysis shows that our protocol is secure against both participant and outsider attack.

Quantum teleportation through noisy channels with multi-qubit GHZ states

We investigate two-party quantum teleportation through noisy channels for multi-qubit Greenberger-Horne-Zeilinger (GHZ) states and find which state loses less quantum information in the process. The dynamics of states is described by the master equation with the noisy channels that lead to the quantum channels to be mixed states. We analytically solve the Lindblad equation for $n$-qubit GHZ states $n\in\{4,5,6\}$ where Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Using the average fidelity we show that 3GHZ state is more robust than $n$GHZ state under most noisy channels. However, $n$GHZ state preserves same quantum information with respect to EPR and 3GHZ states where the noise is in $x$ direction in which the fidelity remains unchanged. We explicitly show that Jung ${\it et\, al.}$ conjecture [Phys. Rev. A ${\bf 78}$, 012312 (2008)], namely, "average fidelity with same-axis noisy channels are in general larger than average fidelity with different-axis noisy channels" is not valid for 3GHZ and 4GHZ states.

Two-party quantum privacy comparison with polarization-entangled bell states and the coherent states

We propose a protocol of quantum privacy comparison with polarization-entangled Bell states and the coherent states. One of two legitimate participants, Alice, prepares polarization-entangled Bell states and keeps one photon of each photon pair and sends the other photons to the third party, Charlie. Receiving the photons, Charlie performs single-photon transformation operations on them and then sends them to the other legitimate participant, Bob. Three participants adopt parity analysis method to check the distribution security of Bell states. Exploiting polarization beam splitters and non-linear interactions mediated by the probe coherent states in Kerr media, Alice and Bob check the parities of their photons using the bases of {|H〉, |V〉} or {|+〉, |-〉}. On the basis of the parity analysis outcomes and Charlie's publicized information, they can analyze the security of the distributed quantum channel. Confirming secure distribution of the shared Bell states, two participants perform respective parity measurements on the privacy photons and own photons of Bell states, and then send the results to Charlie. According to information provided by two legitimate participants and his single-qubit transformation operations, Charlie compares the privacy information of Alice and Bob and publicizes the conclusion.

Parallel Approximation of Min-Max Problems

This paper presents an efficient parallel approximation scheme for a new class of min-max problems. The algorithm is derived from the matrix multiplicative weights update method and can be used to find near-optimal strategies for competitive two-party classical or quantum interactions in which a referee exchanges any number of messages with one party followed by any number of additional messages with the other. It considerably extends the class of interactions which admit parallel solutions, demonstrating for the first time the existence of a parallel algorithm for an interaction in which one party reacts adaptively to the other. As a consequence, we prove that several competing-provers complexity classes collapse to PSPACE such as QRG(2), SQG and two new classes called DIP and DQIP. A special case of our result is a parallel approximation scheme for a specific class of semidefinite programs whose feasible region consists of lists of semidefinite matrices that satisfy a transcript-like consistency condition. Applied to this special case, our algorithm yields a direct polynomial-space simulation of multi-message quantum interactive proofs resulting in a first-principles proof of QIP=PSPACE.

Several teleportation schemes of an arbitrary unknown multi-particle state via different quantum channels

We first provide four new schemes for two-party quantum teleportation of an arbitrary unknown multi-particle state by using three-, four-, and five-particle states as the quantum channel, respectively. The successful probability and fidelity of the four schemes reach 1. In the first two schemes, the receiver can only apply one of the unitary transformations to reconstruct the original state, making it easier for these two schemes to be directly realized. In the third and fourth schemes, the sender can preform Bell-state measurements instead of multipartite entanglement measurements of the existing similar schemes, which makes real experiments more suitable. It is found that the last three schemes may become tripartite controlled teleportation schemes of teleporting an arbitrary multi-particle state after a simple modification. Finally, we present a new scheme for three-party sharing an arbitrary unknown multi-particle state. In this scheme, the sender first shares three three-particle GHZ states with two agents. After setting up the secure quantum channel, an arbitrary unknown multi-particle state can be perfectly teleported if the sender performs three Bell-state measurements, and either of two receivers operates an appropriate unitary transformation to obtain the original state with the help of other receiver's three single-particle measurements. The successful probability and fidelity of this scheme also reach 1. It is demonstrated that this scheme can be generalized easily to the case of sharing an arbitrary unknown multi-particle state among several agents.

Analytical progress on symmetric geometric discord: Measurement-based upper bounds

Quantum correlations may be measured by means of the distance of the state to the subclass of states $\Omega$ having well defined classical properties. In particular, a geometric measure of asymmetric discord [Dakic et al., Phys. Rev. Lett. 105, 190502 (2010)] was recently defined as the Hilbert-Schmidt distance of a given two-qubit state to the closest classical-quantum (CQ) correlated state. We analyze a geometric measure of symmetric discord defined as the Hilbert-Schmidt distance of a given state to the closest classical-classical (CC) correlated state. The optimal member of $\Omega$ is just specially measured original state both for the CQ and CC discords. This implies that this measure is equal to quantum deficit of post-measurement purity. We discuss some general relations between the CC discords and explain why an analytical formula for the CC discord, contrary to the CQ discord, can hardly be found even for a general two-qubit state. Instead of such exact formula, we find simple analytical measurement-based upper bounds for the CC discord which, as we show, are very efficient in the case of two qubits and may serve as independent indicators of two-party quantum correlations. In particular, we propose an adaptive upper bound, which corresponds to the optimal states induced by single-party measurements: optimal measurement on one of the parties determines an optimal measurement on the other party. We discuss how to refine the adaptive upper bound by nonoptimal single-party measurements and by an iterative procedure which usually rapidly converges to the CC discord. We also raise the question of optimality of the symmetric measurements realising the CC discord on symmetric states, and give partial answer for the qubit case.

Long distance two-party quantum crypto made simple

Any two-party cryptographic primitive can be implemented using quantum communication under the assumption that it is difficult to store a large number of quantum states perfectly. However, achieving reliable quantum communication over long distances remains a difficult problem. Here, we consider a large network of nodes with only neighboring quantum links. We exploit properties of this cloud of nodes to enable any two nodes to achieve security even if they are not directly connected. Our results are based on techniques from classical cryptography and do not resort to technologically difficult procedures like entanglement swapping. More precisely, we show that oblivious transfer can be achieved in such a network if and only if there exists a path in the network between the sender and the receiver along which all nodes are honest. Finally, we show that useful notions of security can still be achieved when we relax the assumption of an honest path. For example, we show that we can combine our protocol for oblivious transfer with computational assumptions such that we obtain security if either there exists an honest path, or, as a backup, at least the adversary cannot solve a computational problem.

A protocol for the secure two-party quantum scalar product

A protocol for the secure two-party quantum scalar product

Research of secure two-party quantum comparing protocol

Secure two-party comparing problem is used to compare two private integer without further leaking of information. But in case of the quantum computer the currently available solutions become useless. A secure two-party quantum comparing protocol in semi-honest model is presented based on the a quantum implicit module n+1 addition. The security of the protocol is analyzed.

An Efficient Protocol for the Secure Multi-party Quantum Summation

In this paper, a new and efficient quantum protocol which allows a group of mutually distrustful players to perform the summation computation is proposed. Different from previous protocols, we utilize the multi-particle entangled states as the information carriers. A third party, i.e. TP, is assumed semi-honest in the two-party quantum summation protocol. All various kinds of outside attacks and participant attacks are discussed in detail. In addition, we code all players’ Bell-basis measurement outcomes into one classical bit (cbit). Not only the cost of classical information in the public communication network is decreased, but also the security of the protocol is improved. The protocol is also generalized into multi-party quantum summation. It is secure for the collusive attack performed by at most n−2 players.

Secure quantum private comparison

We propose a two-party quantum private comparison protocol using single photons, in which two distrustful parties can compare whether their secrets are equal with the help of a third party (TP). Any information about the values of their respective secrets will not be leaked out even with a compromised TP. Security is also discussed.

A property of quantum relative entropy with an application to privacy in quantum communication

We prove the following information-theoretic property about quantum states. Substate theorem: Let ρ and σ be quantum states in the same Hilbert space with relative entropy S (ρ ‖ σ) ≔ Tr ρ (log ρ - log σ) = c . Then for all ϵ > 0, there is a state ρ′ such that the trace distance ‖ρ′ - ρ‖ tr : Tr √(ρ′ - ρ) 2 ≤ ϵ, and ρ′/2 O ( c /ϵ 2 ) ≤ σ. It states that if the relative entropy of ρ and σ is small, then there is a state ρ′ close to ρ, i.e. with small trace distance ‖ρ′ - ρ‖ tr , that when scaled down by a factor 2 O ( c ) ‘sits inside’, or becomes a ‘substate’ of, σ. This result has several applications in quantum communication complexity and cryptography. Using the substate theorem, we derive a privacy trade-off for the set membership problem in the two-party quantum communication model. Here Alice is given a subset A ⊆ [ n ], Bob an input i ∈ [ n ], and they need to determine if i ∈ A . Privacy trade-off for set membership: In any two-party quantum communication protocol for the set membership problem, if Bob reveals only k bits of information about his input, then Alice must reveal at least n /2 O( k ) bits of information about her input. We also discuss relationships between various information theoretic quantities that arise naturally in the context of the substate theorem.

An efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement

Following some ideas of the quantum secret sharing (QSS) protocol (2008, Phys. Lett. A 372, 1957), we propose an efficient quantum private comparison (QPC) protocol for comparing information of equality with the help of a third party (TP). The protocol can ensure fairness, efficiency and security. The protocol is fair, which means that one party knows the sound result of the comparison if and only if the other one knows the result. The protocol is efficient with the help of the TP for calculating. However, the TP cannot learn any information about the players' respective private inputs and even about the comparison result and cannot collude with any player. The protocol is secure for the two players, that is, any information about their respective secret inputs will not leak except the final computation result. A precise proof of security of the protocol is presented. Applications of this protocol may include private bidding and auctions, secret ballot elections, commercial business, identification in a number of scenarios and so on.

Greenberger-Horne-Zeilinger versusWstates: Quantum teleportation through noisy channels

Which state loses less quantum information between Greenberger-Horne-Zeilinger (GHZ) and $W$ states when they are prepared for two-party quantum teleportation through a noisy channel? We address this issue by solving analytically a master equation in the Lindblad form with introducing the noisy channels that cause the quantum channels to be mixed states. It is found that the answer to this question is dependent on the type of noisy channel. If, for example, the noisy channel is $({L}_{2,x},{L}_{3,x},{L}_{4,x})$ type, where the $L$'s denote the Lindblad operators, the GHZ state is always more robust than the $W$ state, i.e., the GHZ state preserves more quantum information. In, however, the $({L}_{2,y},{L}_{3,y},{L}_{4,y})$-type channel the situation becomes completely reversed. In the $({L}_{2,z},{L}_{3,z},{L}_{4,z})$-type channel, the $W$ state is more robust than the GHZ state when the noisy parameter $(\ensuremath{\kappa})$ is comparatively small while the GHZ state becomes more robust when $\ensuremath{\kappa}$ is large. In isotropic noisy channel we found that both states preserve an equal amount of quantum information. A relation between the average fidelity and entanglement for the mixed state quantum channels are discussed.