Deterministic Quantum Key Distribution Research Articles

Single-Photon-Memory Two-Step Quantum Secure Direct Communication Relying on Einstein-Podolsky-Rosen Pairs

Quantum secure direct communication (QSDC) is an important branch of quantum communication that is capable of directly transmitting secret messages over a quantum channel. It may be viewed as a concrete realization of Wyner's wiretap channel theory, which ensures the reliable and secure communication of information in the presence of noise and eavesdropping. Hence it is a fully-fledged quantum-communications protocol, which does not require a separate secret key negotiation phase. By contrast, its quantum key distribution (QKD) counterpart represents a secret key-negotiation protocol, which has to be followed up by a separate classical communication session. The essential difference between these two modes of quantum communication lies in the employment of a block-based data transmission technique, proposed by Long and Liu in 2000. However, the original block-based data transmission requires quantum memory, which is not widely available at the time of writing. Recently, this difficulty has been overcome by using classical coding theory, which has been successfully applied to the single-qubit DL04 QSDC. Here we will present a single-photon-memory QSDC protocol based on entangled pairs of photons. We commence by comparing QSDC to QKD, followed by an example of the single-photon QSDC and single-photon QKD protocol. Then we continue by modifying the so-called two-step QSDC protocol designed for deterministic QKD by reducing the number of qubits in a block into a single one, in which Alice prepares Einstein-Podolsky-Rosen (EPR) photon pairs and partitions them into two parts: the so-called pioneer qubit and the follow-up qubit. The pioneer photon is transferred first to Bob, while the follow-up photon is used either for performing encoding or for eavesdropping detection. Bob extracts the candidate key by combining the two particles of the EPR pair to perform Bell-basis measurement. Then the protocol is transformed into a single-photon-memory QSDC using coding theory. Our theoretical analysis shows that the resultant protocol is robust to individual attacks. Additionally, a high communication efficiency is achieved.

Measurement-device-independent quantum secure direct communication

Quantum secure direct communication (QSDC) is a unique technique, which supports the secure transmission of confidential information directly through a quantum channel without the need for a secret key and for ciphertext. Hence this secure communication protocol fundamentally differs from its conventional counterparts. In this article, we report the first measurement-device-independent (MDI) QSDC protocol relying on sequences of entangled photon pairs and single photons. Explicitly, it eliminates the security loopholes associated with the measurement device. Additionally, this MDI technique is capable of doubling the communication distance of its conventional counterpart operating without using our MDI technique. We also conceive a protocol associated with linear optical Bell-basis measurements, where only two of the four Bell-basis states could be measured. When the number of qubits in a sequence reduces to 1, the MDI-QSDC protocol degenerates to a deterministic MDI quantum key distribution protocol.

Two-way quantum key distribution in a uniformly distributed quantum space via a special mapping and its analytical security proofs

Within the field of quantum cryptography, two-way direct quantum secure communication is a relatively new proposal for sharing secret information that is not fully explored yet. We propose a general model for two-way deterministic quantum key distribution, and a special mapping from integers to a uniformly distributed quantum space is introduced for qubit pad preparation. A reduced model, more practical, is also proposed by relaxing the security assumption of the qubit pad preparation. The main work of this paper focuses on the security proofs of these two models. Under collective attacks, we fully analyze the security basis of the general model, and, in a relatively simple way, we provide an analytical security proof for the reduced model in a depolarization quantum channel. Our results show exactly the analytical upper-bound of the amount of useful key that a powerful eavesdropper could extract in both models, and the security of the reduced model is not reduced. One advantage of this work is that the special mapping guarantees the random distribution property of the qubit pad in a uniformly distributed quantum space, thus guaranteeing the security of the two models, and the other advantage is the simplicity of the analytical derivations of security proofs.

Ambiguous discrimination among linearly dependent quantum states and its application to two-way deterministic quantum key distribution

It is impossible to distinguish a set of linearly dependent quantum states, which ensures the security of quantum key distribution (QKD). When considering some features such as symmetry, one may distinguish a part of the quantum states from another part, called ambiguous discrimination. In this paper, we demonstrate that two-way deterministic QKD (TDQKD) is immune to photon-number-splitting (PNS) attacks for two-photon signals. When there are three or more photons in signals, the eavesdropper can gain the key bits probabilistically, without introducing any error rate. When the average number of photons per pulse takes the value of 0.1, the successful probability of PNS attacks on nonempty pulses is about 0.001, and the corresponding channel loss is about 30 dB. Our results show that TDQKD is robust against PNS attacks.

Ping-pong protocol based on the orbital angular momentum of light

Orbital angular momentum (OAM) is one of the photon’s degrees of freedom in infinite-dimensional Hilbert space. In this paper, we use this photon property to propose a modified version of the deterministic two-way quantum key distribution protocol, known as ping-pong protocol, based on the OAM of light. The advantage of the protocol is that it does not require Bell measurement for decoding the information being transmitted, which makes the protocol more flexible and feasible for practical applications. We propose an implementation setup and show how the channel capacity of the protocol can be easily increased. The security of the protocol is analyzed and the probability of detecting Eve in a general incoherent attack is obtained.

Deterministic and Efficient Quantum Key Distribution Using Entanglement Parity Bits and Ancillary Qubits

In this paper, we propose an efficient and deterministic quantum key distribution protocol for establishing a secret key between two untrusted users. In this protocol, a secret key is distributed to a sender and a receiver who share entangled states with a third trusted party but not with each other. This secret key is distributed by the means of special pure quantum states using remote state preparation and controlled gates. In addition, we employ the parity bits of the entangled pairs and the ancillary states to assist in preparing and measuring the secret states. Distributing a state to two users requires two maximally entangled pairs as the quantum channel and a two-particle von Neumann projective measurement. The proposed protocol is exact and deterministic. It distributes a secret key of $ d $ qubits by the means of $ 2d $ entangled pairs and, on average, $ d $ bits of classical communication. We demonstrate the security of this protocol against entanglement attacks and present a method of privacy amplification.

Experimental demonstration on the deterministic quantum key distribution based on entangled photons.

As an important resource, entanglement light source has been used in developing quantum information technologies, such as quantum key distribution(QKD). There are few experiments implementing entanglement-based deterministic QKD protocols since the security of existing protocols may be compromised in lossy channels. In this work, we report on a loss-tolerant deterministic QKD experiment which follows a modified “Ping-Pong”(PP) protocol. The experiment results demonstrate for the first time that a secure deterministic QKD session can be fulfilled in a channel with an optical loss of 9 dB, based on a telecom-band entangled photon source. This exhibits a conceivable prospect of ultilizing entanglement light source in real-life fiber-based quantum communications.

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.

Two-way deterministic quantum key distribution against passive detector side channel attacks in the forward line

In the four-state two-way deterministic quantum key distribution (DQKD) protocol, Bob prepares a qubit randomly in one of four states and sends it to Alice. Alice encodes her key bit on the arrival qubit and returns it to Bob who measures the redux qubit to decode Alice's key bit in a deterministic manner, without basis reconciliation. The unconditional security of the final key of this protocol has been proven in the ideal-device settings. Recently, it has been proven that two-way DQKD protocol is immune to all detector side channel attacks in the backward line A-to-B. In this paper, we study the security of two-way DQKD against passive detector side channel attacks in the forward line B-to-A. In a passive detector side channel attack, the eavesdropper Eve does not disturb quantum state of travel photon but utilizes the efficiency mismatch of two single-photon detectors to estimate the value of key bits, such as the time-shift attack. We prove that two-way DQKD is immune against all passive detector side channel attacks in the forward line B-to-A, although such attacks are efficient on BB84 protocol.

Quantum secure direct communication

Quantum secure direct communication (QSDC) is one of the most important branches of quantum communication. In contrast to the quantum key distribution (QKD) which distributes a secure key between distant parties, QSDC directly transmits secret message instead of sharing key in advance. To establish a secure QSDC protocol, on the one hand, the security of the quantum channel should be confirmed before the exchange of the secret message. On the other hand, the quantum state should be transmitted in a quantum data block since the security of QSDC is based on the error rate analysis in the theories on statistics. Compared with the deterministic quantum key distribution (DQKD) which can also be used to transmit deterministic information, QSDC schemes do not need extra classical bits to read the secret message except for public discussion. In this article, we introduce the basic principles of QSDC and review the development in this field by introducing typical QSDC protocols chronologically. The first QSDC protocol was proposed by Long and Liu, which can be used to establish a common key between distant parties. In their scheme, the method for transmitting quantum states in a block by block way and in multiple steps was proposed and the information leakage before eavesdropping detection was solved. Subsequently, Deng et al. presented two pioneering QSDC schemes, an entangled-state-based two-step QSDC scheme and a single-photon-state-based quantum one-time pad scheme, in which the basic principle and criteria for QSDC were pointed out. From then on, many interesting QSDC schemes have been proposed, including the high-dimension QSDC scheme based on quantum superdense coding, multi-step QSDC scheme based on Greenberger-Horne-Zeilinger states, QSDC scheme based on quantum encryption with practical non-maximally entangled quantum channel, and so on. We also introduce the anti-noise QSDC schemes which were designed for coping with the collective-dephasing noise and the collective-rotation noise, respectively. In 2011, Wang et al. presented the first QSDC which exploited the hyperentangled state as the information carrier and several QSDC schemes based on the spatial degree of freedom (DOF) of photon, single-photon multi-DOF state and hyperentanglement were proposed subsequently. In addition to the point-to-point QSDC schemes, we also review the QSDC networks. Finally, a perspective of QSDC research is given in the last section.

A continuous variable quantum deterministic key distribution based on two-mode squeezed states

The distribution of deterministic keys is of significance in personal communications, but the existing continuous variable quantum key distribution protocols can only generate random keys. By exploiting the entanglement properties of two-mode squeezed states, a continuous variable quantum deterministic key distribution (CVQDKD) scheme is presented for handing over the pre-determined key to the intended receiver. The security of the CVQDKD scheme is analyzed in detail from the perspective of information theory. It shows that the scheme can securely and effectively transfer pre-determined keys under ideal conditions. The proposed scheme can resist both the entanglement and beam splitter attacks under a relatively high channel transmission efficiency.

Two-way deterministic quantum key distribution against detector-side-channel attacks

In a two-way deterministic quantum key distribution (DQKD) protocol, Bob randomly prepares qubits in one of four states and sends them to Alice. To encode a bit, Alice performs an operation on each received qubit and returns it to Bob. Bob then measures the backward qubits to learn about Alice's operations and hence the key bits. Recently, we proved the unconditional security of the final key of this protocol in the ideal device setting. In this paper, we prove that two-way DQKD protocols are immune to all detector side channel attacks at Bob's side, while we assume ideal detectors at Alice's side for error testing. Our result represents a step forward in making DQKD protocols secure against general detector side channel attacks.

A Quantum based Challenge-Response User Authentication Scheme over Noiseless Channel

In this paper, we propose a quantum user authentication protocol witha single photon based on short shared secret key and quantum bit error ratio verification. In this scheme, usage of proposed deterministic quantum key distribution technique and simple v erification in a public channel culminate reduced photon transmission. Security's analysis proves proposed scheme is resistant to impostors’ attacks and eavesdropper. Furthermore , proposed protocol can extend to multiparty environment and permits to re-use many times of the shared secret key without revealing it .

Quantum key distribution with delayed privacy amplification and its application to the security proof of a two-way deterministic protocol

Privacy amplification (PA) is an essential post-processing step in quantum key distribution (QKD) for removing any information an eavesdropper may have on the final secret key. In this paper, we consider delaying PA of the final key after its use in one-time pad encryption and prove its security. We prove that the security and the key generation rate are not affected by delaying PA. Delaying PA has two applications: it serves as a tool for significantly simplifying the security proof of QKD with a two-way quantum channel, and also it is useful in QKD networks with trusted relays. To illustrate the power of the delayed PA idea, we use it to prove the security of a qubit-based two-way deterministic QKD protocol which uses four states and four encoding operations.

Continuous-variable quantum deterministic key distribution protocol based on quantum teleportation

By exploiting quantum teleportation, we propose a continuous-variable quantum deterministic key distribution (CVQDKD) protocol using two-mode squeezed vacuum state and coherent state. The efficiency is 100% under the homodyne detection. The security of CVQDKD is analyzed in detail from information theory, and the result shows that the proposed protocol can securely hand over the pre-deterministic key. By contrast with the quantum random key distribution, the quantum deterministic key distribution plays an irreplaceable role in the field of key management. Furthermore, the CVQDKD can obtain a higher rate and better efficiency than the quantum deterministic key distribution protocols with discrete variables, and the quantum states used in the protocol are also easy to produce and manipulate, which i suitable for long-distance transmission. Therefore, the CVQDKD protocol is more practical.

Tripartite quantum deterministic key distribution based on GHZ states

By exploiting the entanglement properties of continuous variable quantum GHZ state, we propose a tripartite quantum deterministic key distribution, in which the key is generated from its amplitude and the phase can be used to test and verify the channel security. The existing quantum deterministic key distribution can only hand over deterministic key to one receiver in one communication. However, we always have to transmit deterministic key to more than one receiver in real life. The analysis results of information theory show that when the channel transmission efficiency is greater than 0.5, the proposed protocol can securely hand over the pre-deterministic key to two receivers simultaneously, and it can also be extended to multiparty quantum deterministic key distribution when preparing multiple entangled state, this will greatly improve the overall efficiency of the key transmission, furthermore, the continuous variable quantum GHZ state could have a higher channel capacity, so the protocol has the important practical significance.

Unconditional security proof of a deterministic quantum key distribution with a two-way quantum channel

In a deterministic quantum key distribution (DQKD) protocol with a two-way quantum channel, Bob sends a qubit to Alice who then encodes a key bit onto the qubit and sends it back to Bob. After measuring the returned qubit, Bob can obtain Alice's key bit immediately, without basis reconciliation. Since an eavesdropper may attack the qubits traveling on either the Bob-Alice channel or the Alice-Bob channel, the security analysis of DQKD protocol with a two-way quantum channel is complicated and its unconditional security has been controversial. This paper presents a security proof of a single-photon four-state DQKD protocol against general attacks.

Deterministic Quantum Key Distribution Using Gaussian-Modulated Squeezed States

A continuous variable ping-pong scheme, which is utilized to generate deterministic private key, is proposed. The proposed scheme is implemented physically by using Gaussian-modulated squeezed states. The deterministic characteristic, i.e., no basis reconciliation between two parties, leads a nearly two-time efficiency comparing to the standard quantum key distribution schemes. Especially, the separate control mode does not need in the proposed scheme so that it is simpler and more available than previous ping-pong schemes. The attacker may be detected easily through the fidelity of the transmitted signal, and may not be successful in the beam splitter attack strategy.

Quantum deterministic key distribution protocols based on teleportation and entanglement swapping

The distribution of the deterministic key has great significance in quantum communication. By exploiting quantum teleportation and entanglement swapping, two quantum deterministic key distribution (QDKD) protocols are presented to hand over the previously deterministic key to the intended receiver, which is different from the existed quantum key distribution (QKD) protocols only yielding a random key. Meanwhile, the proposed QDKD protocol based on teleportation can also distribute the random key. Furthermore, the security of QDKD protocols is analyzed in detail from information theory. It shows that our proposed QDKD protocols can securely and effectively hand over the pre-deterministic key to the specific target. The QDKD protocols are the necessary supplement to the QKD protocols generating random key and of great significance in the field of key management.

Attack with Hong–Ou–Mandel interferometer to quantum key distribution

We suggest a sophisticated attack protocol, which can be applied to the two-way deterministic quantum key distribution protocol. When more than two photons are used for a qubit, Eve picks out a photon each from the forward and the backward channel and measures whether the states of the two picked-out photons are orthogonal or the same by using the fourth order quantum interference. We describe the attack protocol, which uses an active arrangement of two Hong–Ou–Mandel interferometers combined with further quantum nondemolition measurements, beam splitters, and polarization rotator.