Quantum Inf Research Articles

Cryptanalysis and improvement in semi-quantum private comparison based on Bell states

Recently, Jiang proposed a semi-quantum private comparison (SQPC) protocol without the use of a quantum measurement device (Quantum Inf Process 19:182, 2020). However, this paper highlights a security loophole during the transmission phase of the protocol in which a malicious participant can perform a double CNOT attack to steal partial information of the other participant’s private secret without being detected. With the same assumption of the semi-quantum environment as Jiang’s protocol, this paper presents an improved protocol by adopting a strategy of pre-sharing session keys to overcome the double CNOT attack. Moreover, a security analysis of the collective attack is also provided for Jiang’s and the improved SQPC protocols.

New flexible quantum private query protocol against rotation noise

The quantum privacy query protocol (QPQ) is faced with low query efficiency, transmission channel noise, and low transmission efficiency problems. The quantum-privacy query protocol proposed by us aims to achieve a better quantum-privacy block query effect and has the function of anti-rotation noise. To solve the collective rotation noise in the transmission channel, we propose a one-way QPQ protocol based on four particles. The four-particle states { $$\left| {\phi_{0} } \right\rangle$$ , $$\left| {\phi_{1} } \right\rangle$$ , $$\left| {\phi_{0} ^{\prime}} \right\rangle$$ , $$\left| {\phi_{1} ^{\prime}} \right\rangle$$ } can be entangled by two Bell states { $$\left| {\Phi^{ + } } \right\rangle ,\left| {\Psi^{ - } } \right\rangle$$ } with anti-noise properties. In general, the unidirectional quantum privacy query has more advantages than a bidirectional quantum privacy query. Besides, the post-processing scheme Yang et al. (Quantum Inf Process 15(9):38333840, 2016) can not only protect the parity result of the random key but also guarantee the security of the protocol. In the security analysis, we prove the security of the user and database.

A note on “new quantum key agreement protocols based on Bell states”

We remark that the quantum key agreement protocol (Yang et al. in Quantum Inf Process 18(10):322, 2019) is flawed. It is unnecessary for Bob to prepare his secret key $$K_B$$ , because it is finally announced and accessible to adversaries. We find, $$K_B$$ has no relation to the confidentiality of the final agreed key $$K_{AB}=K_A\oplus K_B$$ . It is just a key transfer scheme, not a general key agreement scheme. We also find there is short of a code for Bob to extract bits from the measured results.

Sum uncertainty relations based on metric-adjusted skew information

We show that the sum uncertainty relations for Wigner–Yanase skew information introduced in Chen et al. (Quantum Inf Process 15:2639–2648, 2016) can hold for an arbitrary metric adjusted skew information. A refinement of one main result in that paper is formulated via a series of lower bounds consisting of the skew information of any prescribed size of the combinations. We also study the metric-adjusted skew information-based uncertainty relations for quantum channels in the spirit of Fu et al. (Quantum Inf Process 18:258, 2019).

Cyclic quantum teleportation via G-states

In 2017, Chen et al. [Quantum Inf. Process. 16 (2017) 201] proposed a scheme for cyclic quantum teleportation (CYQT) of three single-qubit information states among three participants by using six-qubit entangled state as a quantum channel. Following the work of Chen et al., we propose a new scheme for CYQT in which four participants cyclically teleport four arbitrary single-qubit information states among themselves by using two [Formula: see text]-states as a quantum channel. In our scheme, reverse CYQT can also be realized throughout changing the qubit pairs to be measured by each participant. We also generalize our scheme for CYQT of [Formula: see text]-qubit entangled states.

Error-correction and noise-decoherence thresholds for coherent errors in planar-graph surface codes

We numerically study coherent errors in surface codes on planar graphs, focusing on noise of the form of $Z$- or $X$-rotations of individual qubits. We find that, similarly to the case of incoherent bit- and phase-flips, a trade-off between resilience against coherent $X$- and $Z$-rotations can be made via the connectivity of the graph. However, our results indicate that, unlike in the incoherent case, the error-correction thresholds for the various graphs do not approach a universal bound. We also study the distribution of final states after error correction. We show that graphs fall into three distinct classes, each resulting in qualitatively distinct final-state distributions. In particular, we show that a graph class exists where the logical-level noise exhibits a decoherence threshold slightly above the error-correction threshold. In these classes, therefore, the logical level noise above the error-correction threshold can retain significant amount of coherence even for large-distance codes. To perform our analysis, we develop a Majorana-fermion representation of planar-graph surface codes and describe the characterization of logical-state storage using fermion-linear-optics-based simulations. We thereby generalize the approach introduced for the square lattice by Bravyi \textit{et al}. [npj Quantum Inf. 4, 55 (2018)] to surface codes on general planar graphs.

Cryptanalysis and Improvement on Authenticated Semi-quantum Direct Communication Protocol using Bell States

Luo and Hwang [Quantum Inf. Process (2016) 15:947–958] proposed the authenticated semi-quantum direct communication protocols for a quantum participant to be able to transmit secret messages to a classical participant without employing an authenticated classical channel. However, this study indicates that there is an information leakage problem in Luo and Hwang’s measure-resend protocol. The information leakage problem might allow an attacker to use an intercept-resend attack to obtain partial secret messages. Finally, an improved method is proposed to overcome the information leakage problem.

Cyclic quantum teleportation via GHZ-like state

Following the work of Chen et al. [Quantum Inf. Process. 16, 201 (2017)] and Zhang [Mod. Phys. Lett. A 34, 1950290 (2019)], we propose a scheme for cyclic quantum teleportation (CYQT) in which three participants Alice, Bob and Charlie can teleport three arbitrary single-qubit information states cyclically among themselves by using GHZ-like states. Chen et al. and Zhang proposed schemes for CYQT and bidirectional quantum teleportation (BQT) involving three participants, respectively. In the scheme of Chen et al., the quantum teleportation (QT) can be realized successfully between any two participants without the help of third participants and in Zhang’s scheme, two unknown single-qubit states are teleported bidirectionally between two participants with the help of a third participant. On the other hand, in our proposed scheme, all the three participants are controller as well as sender and receiver. The teleportation processes Alice [Formula: see text] Bob, Bob [Formula: see text] Charlie and Charlie [Formula: see text] Alice are controlled by Charlie, Alice and Bob, respectively, and hence the CYQT could not be realized successfully without the cooperation of all three participants. If any one participant denies to cooperate with other two participants, then the CYQT cannot be realized successfully.

Bidirectional quantum teleportation of two-qubit entangled state by using G-state as a quantum channel

In this paper, we propose a new scheme for faithful bidirectional quantum teleportation (BQT) of special type of two-qubit entangled states by using single G state as a quantum channel. In 2016, by using five-qubit and six-qubit entangled states as the quantum channels, two different BQT schemes were proposed by Sang ((2016) Int. J. Theor. Phys. 55, 1333) and Hassanpour et al ((2016) Quantum Inf. Process. 15, 905) respectively. In first scheme, Alice teleports a special type of two-qubit entangled state to Bob and at the same time Bob teleports a single qubit state to Alice. In later scheme, Alice and Bob teleport special type of two-qubit entangled state to each other simultaneously. In contrast to these schemes, in our proposed scheme Alice and Bob can teleport special type of two-qubit entangled states to each other simultaneously while the quantum channel is a four-qubit entangled state. Our proposed BQT scheme requires minimum consumption of quantum and classical resources and it has maximum intrinsic efficiency as compared with previous BQT schemes. We also generalize our scheme for bidirectional quantum teleportation of N-qubit entangled states.

Cryptanalysis and improvement of Wu–Cai–Wu–Zhang’s quantum private comparison protocol

In a recent paper [Int. J. Quantum Inf. 17 (2019) 1950026], the authors discussed the shortcomings in the security of a quantum private comparison protocol that we previously proposed [Int. J. Quantum Inf. 15 (2017) 1750014]. They also proposed a new protocol aimed to avoid these problems. Here, we analyze the information leaked in their protocol, and find that it is even less secure than our protocol in certain cases. We further propose an improved version which has the following advantages: (1) no entanglement needed, (2) quantum memory is no longer required, and (3) less information leaked. Therefore, better security and great feasibility are both achieved.

Two efficient measurement device independent quantum dialogue protocols

Quantum dialogue is a process of two-way secure and simultaneous communication using a single channel. Recently, a Measurement Device Independent Quantum Dialogue (MDI-QD) protocol has been proposed [A. Maitra, Measurement device independent quantum dialogue,Quantum Inf. Process. 16(12) (2017) 305]. To make the protocol secure against information leakage, the authors have discarded almost half of the qubits remaining after the error estimation phase. In this paper, we propose two modified versions of the MDI-QD protocol such that the number of discarded qubits is reduced to almost one-fourth of the remaining qubits after the error estimation phase. We use almost half of their discarded qubits along with their used qubits to make our protocol more efficient in qubits count. We show that both of our protocols are secure under the same adversarial model given in MDI-QD protocol.

Bounds on the number of mutually unbiased entangled bases

We provide several bounds on the maximum size of MU k-Schmidt bases in $$\mathbb {C}^{d}\otimes \mathbb {C}^{d'}$$ . We first give some upper bounds on the maximum size of MU k-Schmidt bases in $$\mathbb {C}^{d}\otimes \mathbb {C}^{d'}$$ by conversation law. Then we construct two maximally entangled mutually unbiased (MU) bases in the space $$\mathbb {C}^{2}\otimes \mathbb {C}^{3}$$ , which is the first example of maximally entangled MU bases in $$\mathbb {C}^d\otimes \mathbb {C}^{d'}$$ when $$d\not \mid d'$$ . By applying a general recursive construction to this example, we are able to obtain two maximally entangled MU bases in $$\mathbb {C}^{d}\otimes \mathbb {C}^{d'}$$ for infinitely many $$d,d'$$ such that d is not a divisor of $$d'$$ . We also give some applications of the two maximally entangled MU bases in $$\mathbb {C}^{2}\otimes \mathbb {C}^{3}$$ . Further, we present an efficient method of constructing MU k-Schmidt bases. It solves an open problem proposed in [Y. F. Han et al., Quantum Inf. Process. 17, 58 (2018)]. Our work improves all previous results on maximally entangled MU bases.

Four-party quantum operation sharing with composite quantum channel in Bell and Yeo–Chua product state

A four-party single-qubit operation sharing scheme is put forward by utilizing the Bell and Yeo–Chua product state in an entanglement structure as the composite quantum channel. Four features of the scheme are discussed and confirmed, including its determinacy, symmetry, and security as well as the scheme experimental feasibility. Moreover, some concrete comparisons between our present scheme and a previous scheme [H. Xing et al., Quantum Inf. Process. 13 (2014) 1553] are made from the aspects of quantum and classical resource consumption, necessary operation complexity, and intrinsic efficiency. It is found that our present scheme is more superior than that one. In addition, the essential reason why the employed state in the entanglement structure is applicable for sharing an arbitrary single-qubit operation among four parties is revealed via deep analyses. With respect to the essential reason, the capacity of the product state in quantum operation sharing (QOS) is consequently shown by simple presenting the corresponding schemes with the state in other entanglement structures.

Significance of entangling operators in the purview of modified EWL scheme

Recently, a modified approach to Eisert, Wilkens and Lewenstein quantization scheme has been proposed in Vijayakrishnan and Balakrishnan (Quantum Inf Process 18:112, 2019), with an aim to explore the two-qubit entangling operators in the domain of game theory. In the present work, we show the implications of such a modification by considering the possibility of conversion of symmetric to potential game, when one of the players uses a quantum strategy while the other resorts to classical strategy. Secondly, we show that entangling operators which produce same average payoffs do not produce same average entanglement. Furthermore, the converse is also found to hold good. Following which, we show that conversion of symmetric to potential games can be done through operators which are perfect entanglers.

Information leakage in protection of quantum dialogue affected by quantum field

Recently, Huang et al. (Quantum Inf Process 18:37, 2019) proposed a quantum dialogue protocol by using three-qubit GHZ states. We study the security of the proposed protocol and find that it is not secure and has the drawback of information leakage. Finally, we modify only the tenth step in the proposed protocol, so that it can overcome the drawback.

Quantum key distribution with any two independent and identically distributed states

To prove the security of quantum key distribution (QKD) protocols, several assumptions have to be imposed on users' devices. From an experimental point of view, it is preferable that such theoretical requirements are feasible and the number of them is small. In this paper, we provide a security proof of a QKD protocol where the usage of any light source is allowed as long as it emits two independent and identically distributed (i.i.d.) states. Our QKD protocol is composed of two parts: the first part is characterization of the photon-number statistics of the emitted signals up to three-photons based on the method [Opt. Exp. 27, 5297 (2019)], followed by running our differential-phase-shift (DPS) protocol [npj Quantum Inf. 5, 87 (2019)]. It is remarkable that as long as the light source emits two i.i.d. states, even if we have no prior knowledge of the light source, we can securely employ it in the QKD protocol. As this result substantially simplifies the requirements on light sources, it constitutes a significant contribution on realizing truly secure quantum communication.

Improvement of Quantum Protocols for Secure Multi-Party Summation

Secure multi-party quantum summation is an important branch of secure multi-party quantum computation. Recently, Ji et al. suggested a secure multi-party quantum summation scheme based on the entanglement swapping between the d-level Bell state and the d -level n+1-particle cat state (Quantum Inf Process (2019)18:168). In this paper, it is pointed out that Ji et al.’s secure multi-party quantum summation scheme has a security loophole, i.e., the third party (TP) can obtain the secret numbers of n communicants without being discovered. Then, in order to avoid this security loophole, an improvement is suggested by adopting the method of encrypting the secret integers of n communicants with a pre-shared private key sequence among them.

Mixture of Gaussians in the open quantum random walks

We discuss the Gaussian and the mixture of Gaussians in the limit of open quantum random walks. The central limit theorems for the open quantum random walks under certain conditions were proven by Attal et al (Ann Henri Poincare 16(1):15–43, 2015) on the integer lattices and by Ko et al (Quantum Inf Process 17(7):167, 2018) on the crystal lattices. The purpose of this paper is to investigate the general situation. We see that the Gaussian and the mixture of Gaussians in the limit depend on the structure of the invariant states of the intrinsic quantum Markov semigroup whose generator is given by the Kraus operators which generate the open quantum random walks. Some concrete models are considered for the open quantum random walks on the crystal lattices. Due to the intrinsic structure of the crystal lattices, we can conveniently construct the dynamics as we like. Here, we consider the crystal lattices of $$\mathbb {Z}^2$$ with intrinsic two points, hexagonal, triangular, and Kagome lattices. We also discuss Fourier analysis on the crystal lattices which gives another method to get the limit theorems.

Improvement of multi-party quantum private comparison protocol using d-dimensional basis states without entanglement swapping

Recently, Gu et al. (2019, arXiv:1907.02656) and Zhang et al. (Quantum Inf Process (2019)18:336) independently pointed out that in Yang et al.’s quantum summation protocol (Quantum Inf Process (2018) 17:129), the party in charge of preparing the initial quantum states is able to steal other parties’ private integer strings without being discovered by launching two special kinds of attack. In this paper, it is pointed out that in Liu et al.’s MQPC protocol, if the third party (TP) named Calvin launches the similar attacks, she can also steal the private secrets from n parties without being discovered. Then, two methods are put forward to avoid this drawback, i.e., the first one is to add the process of checking whether the quantum states shared among n parties are genuinely in the state of |W〉12⋯n while the second one is to encrypt the private secrets from n parties with a private key sequence shared among them beforehand.

Optimized Bidirectional Quantum Operation Teleportation with Three Bell States

Recently, utilizing three Bell states as quantum channel, Zhou et al. (Int. J. Quantum Inf. 16, 1850042, 2018) presented a novel scheme for bidirectionally teleporting quantum operations. However, their scheme is unsuccessful. To be exact, it actually only realized bidirectional quantum state teleportation other than quantum operation teleportation they claimed. In this paper, we propose an optimized scheme using the same three Bell States. Compared with that of Zhou et al., our scheme can not only realize the real bidirectional quantum operation teleportation, but also be more lower in the terms of complexity of the necessary operations. Additionally, the status of two users in our scheme is equal.