Shor and Preskill have provided a simple proof of security of the standard quantum key distribution scheme by Bennett and Brassard (BB84) by demonstrating a connection between key distribution and entanglement purification protocols with one-way communications. Here we provide proofs of security of standard quantum key distribution schemes, BB84 and the six-state scheme, against the most general attack, by using the techniques of *two*-way entanglement purification. We demonstrate clearly the advantage of classical post-processing with two-way classical communications over classical post-processing with only one-way classical communications in QKD. This is done by the explicit construction of a new protocol for (the error correction/detection and privacy amplification of) BB84 that can tolerate a bit error rate of up to 18.9%, which is higher than what any BB84 scheme with only one-way classical communications can possibly tolerate. Moreover, we demonstrate the advantage of the six-state scheme over BB84 by showing that the six-state scheme can strictly tolerate a higher bit error rate than BB84. In particular, our six-state protocol can tolerate a bit error rate of 26.4%, which is higher than the upper bound of 25% bit error rate for any secure BB84 protocol. Consequently, our protocols may allow higher key generation rate and remain secure over longer distances than previous protocols. Our investigation suggests that two-way entanglement purification is a useful tool in the study of advantage distillation, error correction, and privacy amplification protocols.
The long-standing problem of quantum information processing is to remove the classical channel from quantum communication. Introducing a new information processing technique, it is discussed that both insecure and secure quantum communications are possible without the requirement of classical channel.
We propose the schemes of quantum secure direct communication (QSDC) based on secret transmitting order of particles. In these protocols, the secret transmitting order of particles ensures the security of communication, and no secret messages are leaked even if the communication is interrupted for security. This strategy of security for communication is also generalized to quantum dialogue. It not only ensures the unconditional security but also improves the efficiency of communication.
This paper provides a security proof of the Bennett-Brassard (BB84) quantum key distribution protocol in practical implementation. To prove the security, it is not assumed that defects in the devices are absorbed into an adversary's attack. In fact, the only assumption in the proof is that the source is characterized. The proof is performed by lower-bounding adversary's Renyi entropy about the key before privacy amplification. The bound reveals the leading factors reducing the key generation rate.
Fast development of supercomputer and perspective quantum computer is posing increasing serious threats to communication security. Based on the laws of quantum mechanics, quantum communication offers provable security of communication, and is a promising solution to counter such threats. Quantum secure direct communication (QSDC) is one of the important branches of quantum communication. Different from other branches of quantum communication, it transmits secret information directly. Recently, remarkable progress has been made in the proof-of-principle experimental demonstrations of QSDC. Howe…
We apply the techniques introduced in [Kraus et. al., Phys. Rev. Lett. 95, 080501, 2005] to prove security of quantum key distribution (QKD) schemes using two-way classical post-processing as well as QKD schemes based on weak coherent pulses instead of single-photon pulses. As a result, we obtain improved bounds on the secret-key rate of these schemes.
In the direct communication quantum channels the authorized recipient (Bob) and the non-authorized recipient (Eve) have different abilities for verification of received information. Bob can apply the feedback to commit the sender (Alice) to perform verification. Eve has to use for verification an indirect method based on the measurement of a set of incompatible observables enough for determination of the coding basis used by Alice. In the protocol of direct communication regular modification of coding basis and masking it with an equilibrium in average information carrier density matrix preven…
We prove the security of a high-capacity quantum key distribution protocol over noisy channels. By using entanglement purification protocol, we construct a modified version of the protocol in which we separate it into two consecutive stages. We prove their securities respectively and hence the security of the whole protocol.
We report an experimental implementation of free-space quantum secure direct communication based on single photons. The quantum communication scheme uses phase encoding, and the asymmetric Mach-Zehnder interferometer is optimized so as to automatically compensate phase drift of the photons during their transitions over the free-space medium. An information transmission rate of 500 bps over a 10-meter free space with a mean quantum bit error rate of 0.49%$\pm$0.27% is achieved. The security is analyzed under the scenario that Eve performs collective attack and photon number splitting collective…
It is repeatedly and persistently claimed in the literature that a specific trace criterion $d$ would guarantee universal composition security in quantum cryptography. Currently that is the sole basis of unconditional security claim in quantum key distribution. In this paper, it is shown that just security against known-plaintext attacks when the generated key is used in direct encryption is not provided by $d$. The problem is directly connected with several general problems in the existing unconditional security proofs in quantum key distribution. A number of issues will be clarified concerni…
We describe the popular BB84 protocol and critically examine its security proof as presented by Shor and Preskill. The proof requires the use of quantum error correcting codes called the Calderbank-Shor-Steanne (CSS) quantum codes. These quantum codes are constructed in the quantum domain from two suitable classical linear codes, one used to correct for bit-flip errors and the other for phase-flip errors. Consequently, as a prelude to the security proof, the report reviews the essential properties of linear codes, especially the concept of cosets, before building the quantum codes that are uti…
Although quantum communication systems are being deployed on a global scale, their realistic security certification is not yet available. Here we present a security evaluation and improvement protocol for complete quantum communication systems. The protocol subdivides a system by defining seven system implementation sub-layers based on a hierarchical order of information flow; then it categorises the known system implementation imperfections by hardness of protection and practical risk. Next, an initial analysis report lists all potential loopholes in its quantum-optical part. It is followed b…
Quantum secure direct communication is one of the important mode of quantum communication, which sends secret information through a quantum channel directly without setting up a prior key. Over the past decade, numerous protocols have been proposed, and part of them have been experimentally demonstrated. However, the strict security proof is still in suspense. Two-way protocol is seen as one of the most practical protocol, in this paper, the security of the two-way quantum secure direct communication protocol will be proved against general attacks when the noisy and lossy channel is taken into…
We show the information-theoretic security proof of the differential-phase-shift (DPS) quantum key distribution (QKD) protocol based on the complementarity approach [arXiv:0704.3661 (2007)]. Our security proof provides a slightly better key generation rate compared to the one derived in the previous security proof in [arXiv:1208.1995 (2012)] that is based on the Shor-Preskill approach [Phys. Rev. Lett. ${\bf 85}$, 441 (2000)]. This improvement is obtained because the complementarity approach can employ more detailed information on Alice's sending state in estimating the leaked information to a…
We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol. We then show that the security of this protocol implies the security of BB84. The entanglement-purification based protocol uses Calderbank-Shor-Steane (CSS) codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.
Two-way Gaussian protocols have the potential to increase quantum key distribution (QKD) protocols' secret-key rates by orders of magnitudes~[Phys.~Rev.~A {\bf 94}, 012322 (2016)]. Security proofs for two-way protocols, however, are underdeveloped at present. In this paper, we establish a security proof framework for the general coherent attack on two-way Gaussian protocols in the asymptotic regime. We first prove that coherent-attack security can be reduced to collective-attack security for all two-way QKD protocols. Next, we identify two different constraints that each provide intrusion para…
Quantum Key Distribution (QKD) in principle offers unconditional security based on the laws of physics. Continuous variable (CV) quantum key distribution has the potential for high-key-rate and low-cost implementations using standard telecom components. Despite tremendous theoretical and experimental progress in continuous-variable quantum key distribution, the security has not been rigorously established for most current continuous-variable quantum key distribution systems that have imperfections. Among the imperfections, intensity fluctuation is a significant principal problem affecting secu…
We prove the security of quantum key distribution against the most general attacks which can be performed on the channel, by an eavesdropper who has unlimited computation abilities, and the full power allowed by the rules of classical and quantum physics. A key created that way can then be used to transmit secure messages in a way that their security is also unaffected in the future.
In this paper, we consider a quantum key distribution protocol (QKD) with two-way classical communication that is assisted by one-time pad encryption. We propose a two-way preprocessing that uses one-time pad encryption by previously shared secret key, and the net key rate of the QKD with proposed preprocessing exceeds the key rate of the QKD without it. The preprocessing is reduced to the entanglement distillation protocol with two-way classical communication and previously shared EPR pairs (two-way breeding protocol), and the security of QKD with the preprocessing is guaranteed in the same w…
Recently, Pawlowski [Phys. Rev. A 82, 032313 (2010)] claimed to have proven the security of a quantum key distribution by using only the monogamy of Bell's inequality violations. In the proof, however, he tacitly assumed that the eavesdropper's outcome is binary. The assumption cannot be justified because Eve's (eavesdropper's) power can only be limited by natural principle. We provide a counter-example for a step of the proof.
We give the first composable security proof for continuous-variable quantum key distribution with coherent states against collective attacks. Crucially, in the limit of large blocks the secret key rate converges to the usual value computed from the Holevo bound. Combining our proof with either the de Finetti theorem or the Postselection technique then shows the security of the protocol against general attacks, thereby confirming the long-standing conjecture that Gaussian attacks are optimal asymptotically in the composable security framework. We expect that our parameter estimation procedure, …
We analyzed the security of the secure direct communication protocol based on secret transmitting order of particles recently proposed by Zhu, Xia, Fan, and Zhang [Phys. Rev. A 73, 022338 (2006)], and found that this scheme is insecure if an eavesdropper, say Eve, wants to steal the secret message with Trojan horse attack strategies. The vital loophole in this scheme is that the two authorized users check the security of their quantum channel only once. Eve can insert another spy photon, an invisible photon or a delay one in each photon which the sender Alice sends to the receiver Bob, and cap…
Two protocols of quantum direct communication with authentication [Phys. Rev. A {\bf 73}, 042305 (2006)] are recently proposed by Lee, Lim and Yang. In this paper we will show that in the two protocols the authenticator Trent should be prevented from knowing the secret message of communication. The first protocol can be eavesdropped by Trent using the the intercept-measure-resend attack, while the second protocol can be eavesdropped by Trent using single-qubit measurement. To fix these leaks, I revise the original versions of the protocols by using the Pauli-Z operation $σ_z$ instead of the or…
We discuss long code problems in the Bennett-Brassard 1984 (BB84) quantum key distribution protocol and describe how they can be overcome by concatenation of the protocol. Observing that concatenated modified Lo-Chau protocol finally reduces to the concatenated BB84 protocol, we give the unconditional security of the concatenated BB84 protocol.
Quantum secure direct communication (QSDC) is an important branch of quantum communication that transmits confidential message directly in a quantum channel without utilizing encryption and decryption. It not only prevents eavesdropping during transmission, but also eliminates the security loophole associated with key storage and management. Recently measurement-device-independent (MDI) QSDC protocols in which the measurement is performed by an untrusted party using imperfect measurement devices have been constructed, and MDI-QSDC eliminates the security loopholes originating from the imperfec…
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 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…
From the perspective of information theory and cryptography, we analyze the security of two quantum dialogue protocols and a bidirectional quantum secure direct communication (QSDC) protocol, and point out that the transmitted information would be partly leaked out in them. That is, any eavesdropper can elicit some information about the secrets from the public annunciations of the legal users. This phenomenon should have been strictly forbidden in a quantum secure communication. In fact, this problem exists in quite a few recent proposals and, therefore, it deserves more research attention in …
Differential phase shift quantum key distribution systems have a high potential for achieving high speed key generation. However, its unconditional security proof is still missing, even though it has been proposed for many years. Here, we prove its security against collective attacks with a weak coherent light source in the noiseless case (i.e. no bit error). The only assumptions are that quantum theory is correct, the devices are perfect and trusted and the key size is infinite. Our proof works on threshold detectors. We compute the lower bound of the secret key generation rate using the info…
We present a continuous-variable quantum key distribution protocol combining a discrete modulation and reverse reconciliation. This protocol is proven unconditionally secure and allows the distribution of secret keys over long distances, thanks to a reverse reconciliation scheme efficient at very low signal-to-noise ratio.
A simple proof of the unconditional security of a relativistic quantum cryptosystem based on orthogonal states is proposed. Restrictions imposed by special relativity allow to substantially simplify the proof compared with the non-relativistic cryptosystems involving non-orthogonal states. Important for the proposed protocol is the spatio-temporal structure of the quantum states which is actually ignored in the non-relativistic protocols employing only the structure of the state space of the information carriers. As a consequence, the simplification arises because of the inefficiency of collec…
We derive a proof of security for the Differential Phase Shift Quantum Key Distribution (DPSQKD) protocol under the assumption that Eve is restricted to individual attacks. The security proof is derived by bounding the average collision probability, which leads directly to a bound on Eve's mutual information on the final key. The security proof applies to realistic sources based on pulsed coherent light. We then compare individual attacks to sequential attacks and show that individual attacks are more powerful.
Quantum secure direct communication provides a direct means of conveying secret information via quantum states among legitimate users. The past two decades have witnessed its great strides both theoretically and experimentally. However, the security analysis of it still stays in its infant. Some practical problems in this field to be solved urgently, such as detector efficiency mismatch, side-channel effect and source imperfection, are propelling the birth of a more impeccable solution. In this paper, we establish a new framework of the security analysis driven by numerics where all the practi…
We present an approach to the unconditional security of quantum key distribution protocols based on the uncertainty principle. The approach applies to every case that has been treated via the argument by Shor and Preskill, and relieve them from the constraints of finding quantum error correcting codes. It can also treat the cases with uncharacterized apparatuses. We derive a secure key rate for the Bennett-Brassard-1984 protocol with an arbitrary source characterized only by a single parameter representing the basis dependence.
In optical implementations of the phase-encoded BB84 protocol, the bit information is usually encoded in the phase of two consecutive photon pulses generated in a Mach-Zehnder interferometer. In the actual experimental realization, the loss in the arms of the Mach-Zehnder interferometer is not balanced, for example because only one arm contains a lossy phase modulator. Therefore, the amplitudes of the pulses is not balanced, and the structure of the signals and measurements no longer corresponds to the (balanced) ideal BB84 protocol. Hence, the BB84 security analysis no longer applies in this …
We show a deterministic secure direct communication protocol using single qubit in mixed state. The security of this protocol is based on the security proof of BB84 protocol. It can be realized with current technologies.
We provide security bounds against coherent attacks for two families of quantum key distribution protocols that use $d$-dimensional quantum systems. In the asymptotic regime, both the secret key rate for fixed noise and the robustness to noise increase with $d$. The finite-key corrections are found to be almost insensitive to $d\lesssim 20$.
"Device-independent" not only represents a relaxation of the security assumptions about the internal working of the quantum devices, but also can enhance the security of the quantum communication. In the paper, we put forward the first device-independent quantum secure direct communication (DI-QSDC) protocol, where no assumptions are made about the way the devices work or on what quantum system they operate. We show that in the absence of noise, the DI-QSDC protocol is absolutely secure and there is no limitation for the communication distance. However, under practical noisy quantum channel co…
The security of quantum key distribution (QKD) has been proven for different protocols, in particular for the BB84 protocol. It has been shown that this scheme is robust against eventual imperfections in the state preparation, and sending only three different states delivers the same secret key rate achievable with four states. In this work, we prove, in a finite-key scenario, that the security of this protocol can be maintained even with less measurement operators on the receiver. This allows us to implement a time-bin encoding scheme with a minimum amount of resources.
Rigorous mathematical proofs of the security of continuous-variable quantum key distribution (CV QKD) have been obtained recently. Unfortunately, these security proofs rely on assumptions that are hardly met in experimental practice. Here I investigate these issues in detail, and discuss experimentally-friendly workarounds to assess the security of CV QKD. The aim of this paper is to show that there are hidden and unsolved issues and to indicate possible partial solutions. To provide a complete and rigorous mathematical security proof is out of the scope of this contribution.
We propose a scheme for the secure direct communication based on the entangled phase-coherent states, which shows an elevated level of confidentiality. The protocol gives a simultaneous security control for every bit of transferred information. The security-check-per-bit is provided by sending an additional mode to prove the legitimate parties' authenticity. Other benefit include increased transfer rate, since a separate control sequences is unnecessary. We study the security of the scheme for both ideal and realistic quantum channel. The protocol shows a robust security and prepares 50% proba…
We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. In the security regime, the purification process factorises the overall initial state into a tensor-product state of Alice and Bob, on one side, and Eve on the other side, thus establishing a completely private, albeit noisy, quantum communication channel between Alice and Bob. The security regime is found to coincide for all practical purposes with the purification regime of a two-way recurrence protocol. This makes two-way entanglement …
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…
Recently, a Quantum Key Exchange protocol that uses squeezed states was presented by Gottesman and Preskill. In this paper we give a generic security proof for this protocol. The method used for this generic security proof is based on recent work by Christiandl, Renner and Ekert.
Recently in 2018, Niu et al. proposed a measurement-device-independent quantum secure direct communication protocol using Einstein-Podolsky-Rosen pairs and generalized it to a quantum dialogue protocol (Niu et al., Science bulletin 63.20, 2018). By analyzing these protocols we find some security issues in both these protocols. In this work, we show that both the protocols are not secure against information leakage, and a third party can get half of the secret information without any active attack. We also propose suitable modifications of these protocols to improve the security.
We introduce a general approach for the analysis of a quantum direct communication protocol. The method is based on the investigation of the superoperator acting on a joint system of the communicating parties and the eavesdropper. The introduced method is more versatile than the approaches used so far as it permits to incorporate different noise models in a unified way. Moreover, it make use of a well grounded theory of quantum discrimination for the purpose of estimating the eavesdropper's information gain.
Quantum key distribution (QKD) protocols make it possible for two parties to generate a secret shared key. One of the most important QKD protocols, BB84, was suggested by Bennett and Brassard in 1984. Various proofs of unconditional security for BB84 have been suggested, but the first security proofs were not composable. Here we improve a security proof of BB84 given by [Biham, Boyer, Boykin, Mor, and Roychowdhury, J. Cryptology, 19(4):381-439, 2006] to be composable and match the state-of-the-art results for BB84, and we extend it to prove unconditional security of several variants of the BB8…
We prove the security of theoretical quantum key distribution against the most general attacks which can be performed on the channel, by an eavesdropper who has unlimited computation abilities, and the full power allowed by the rules of classical and quantum physics. A key created that way can then be used to transmit secure messages such that their security is also unaffected in the future.
