On the optimality of individual entangling-probe attacks against BB84 quantum key distribution

Some MIT researchers [Phys. Rev. A 75, 042327 (2007)] have recently claimed that their implementation of the Slutsky-Brandt attack [Phys. Rev. A 57, 2383 (1998); Phys. Rev. A 71, 042312 (2005)] to the BB84 quantum-key-distribution (QKD) protocol puts the security of this protocol “to the test” by simulating “the most powerful individual-photon attack” [Phys. Rev. A 73, 012315 (2006)]. A related unfortunate news feature by a scientific journal [G. Brumfiel, Quantum cryptography is hacked, News @ Nature (april 2007); Nature 447, 372 (2007)] has spurred some concern in the QKD community and among the general public by misinterpreting the implications of this work. The present article proves the existence of a stronger individual attack on QKD protocols with encrypted error correction, for which tight bounds are shown, and clarifies why the claims of the news feature incorrectly suggest a contradiction with the established “old-style” theory of BB84 individual attacks. The full implementation of a quantum cryptographic protocol includes a reconciliation and a privacy-amplification stage, whose choice alters in general both the maximum extractable secret and the optimal eavesdropping attack. The authors of [Phys. Rev. A 75, 042327 (2007)] are concerned only with the error-free part of the so-called sifted string, and do not consider faulty bits, which, in the version of their protocol, are discarded. When using the provably superior reconciliation approach of encrypted error correction (instead of error discard), the Slutsky-Brandt attack is no more optimal and does not “threaten” the security bound derived by Lütkenhaus [Phys. Rev. A 59, 3301 (1999)]. It is shown that the method of Slutsky and collaborators [Phys. Rev. A 57, 2383 (1998)] can be adapted to reconciliation with error correction, and that the optimal entangling probe can be explicitly found. Moreover, this attack fills Lütkenhaus bound, proving that it is tight (a fact which was not previously known).     

Probabilistic generalized controlled order rearrangement encryption and secret splitting using W-class state

Based on the controlled order rearrange encryption (CORE) for quantum key distribution using EPR pairs [Fu.G. Deng, G.L. Long, Phys. Rev. A 68 (2003) 042315], we propose a generalized controlled order rearrangement encryption (GCORE) protocol using non-maximally entangled W-class states with probability, but it also has full efficiency and we compare the similarity and difference with original protocol. Besides, we use this W-class state to split quantum information, thus the scheme is robust against decoherence.     

Quantum Secure Direct Communication Based on Authentication

We propose two schemes of quantum secure direct communication （QADC） combined ideas of user authentication [Phys. Rev. A 73 （2006） 042305] and direct communication with dense coding [Phys. Rev. A. 68 （2003） 042317]. In these protocols, the privacy of authentication keys and the properties of the EPR pairs not only ensure the realization of identity authentication but also further improve the security of communication, and no secret messages are leaked even if the messages were broken.     

High Efficiency of Two Efficient QSDC with Authentication Is at the Cost of Their Security

Two efficient protocols of quantum secure direct communication with authentication [Chin. Phys. Lett. 25 （2008） 2354] were recently proposed by Liu et al. to improve the efficiency of two protocols presented in [Phys. Rev. A 75 （2007） 026301] by four Pauli operations. We show that the high efficiency of the two protocols is at the expense of their security. The authenticator Trent can reach half the secret by a particular attack strategy in the first protocol. In the second protocol, not only Trent but also an eavesdropper outside can elicit half-information about the secret from the public declaration.     

Threshold Quantum Secret Sharing of Secure Direct Communication

We propose a （L, n）-threshold quantum secret sharing protocol of secure direct communication following some ideas of Zhang＇s protocol [Phys. Lett. A 342 （2005） 60] and Tokunaga et al.＇s protocol [Phys. Rev. A 71 （2005） 012314]. The sender distributes the classical secret shares to his or her n agents and each agent owns a secret share in advance. The sender＇s secure direct communication message can be extracted by an agent subset by collaboration in such a way that at least t or more agents can obtain the secret message with the mutual assistances but any t - 1 or fewer agents cannot. In contrast to the previous multiparty quantum secret sharing protocols in which the sender＇s secret message can be recovered only if all the agents collaborate, our protocol is more practical and more flexible.     

Efficient Quantum Secure Direct Communication with Authentication

Two protocols of quantum direct communication with authentication [Phys. Rev. A 73 （2006） 042305] were recently indicated to be insecure against the authenticator Trent attacks [Phys. Rev. A 75 （2007） 026301]. We present two efficient protocols by using four Panli operations, which are secure against inner Trent attacks as well as outer Eve attacks. Finally, we generalize them to multiparty quantum direction communication.     

Efficient Multiparty-to-Multiparty Quantum Secret Sharing via Continuous Variable Operations

The one-to-multiparty quantum secret sharing scheme [Phys. Rev. A 71 （2005） 044301] proposed recently is extended to a multiparty-to-multiparty case. Furthermore, the continuous variable operations are employed in the extended scheme to replace the specific discrete unitary operations used in the original scheme. The complete randomicity of the continuous variable characterizing the unitary operations can ensure the security of secret sharing. Moreover, the present scheme is compared with the recent similar scheme [Phys. Rev. A 72 （2005） 012304]. It is found that the efficiency of the present scheme is n times of that of the previous one.     

Class of Unlockable Bound Entangled States and Their Applications

A class of unlockable bound entangled states and their applications are presented. They can be considered as quasi generalized Smolin states [Phys. Rev. A 63 （2001） 032306], which are the states of N ＋ N qubits. No pure entanglement can be distilled from this class of states by local quantum operations and classical communications. However, if certain parties group together, they become distillable. Although they are bound entangled states, they could be used to achieve some non-trivial tasks, such as quantum secret sharing shown in the study.     

An improved quantum key distribution protocol based on second-order coherence

We improve the quantum key distribution protocol proposed by Pereira et al. [S.F. Pereira, Z.Y. Ou, H.J. Kimble, Phys. Rev. A 62 (2000) 042311], by employing the second-order coherence of optical fields, which can be easy experimentally measured with a Hanbury-Brown and Twiss intensity interferometer. It is shown that eavesdropping can be directly detected without sacrificing extra secret bits as test key. The efficiency of the improved system is enhanced greatly, since no secret bit needs to be discarded.     

Reexamining the security of the improved quantum secret sharing scheme

We find that, in the improvement [S.J. Qin et al., Phys. Lett. A 357 (2006) 101] of the multiparty quantum secret sharing [Z.J. Zhang et al., Phys. Rev. A 71 (2005) 044301], Charlie can solely obtain Alice’s secret messages without Bob’s helps. In other words, the improved secret sharing scheme is still insecure. In the end, we further modify Qin et al. improved three-party quantum secret sharing scheme and make it really secure.     

All-versus-nothing inseparability for two pairs of entangled atoms

It is shown that Cabello’s nonlocality without inequalities for two pairs of singlet states [A. Callebo, Phys. Rev. Lett. 87, 010403 (2001)] can be realized in two pairs of trapped atoms based on Innsbruck ion group. The reasoning mainly lies in that controlled NOT (CNOT) gate can be realized between two atoms in ion trap.     

Re-examining generalized teleportation protocol

We present an explicit generalized protocol for probabilistic teleportation of an arbitrary N-qubit GHZ entangled state via only one non-maximally two-qubit entangled state. Without entanglement concentration, using standard Bell-state measurement and classical communication one cannot teleport the state with unit fidelity and unit probability. We show that by properly choosing the measurement basis it is possible to achieve unity fidelity transfer of the state. Compared with Gordon et al’s protocol [G. Gordon, G. Rigolin, Phys. Rev. A 73 (2006) 042309], this protocol has the advantage of transmitting much less qubits and classical information for teleporting an arbitrary N-qubit GHZ state.     

Remote State Preparation with Genuine Multipartite Entanglement

Enlightened by the work of Yeo and Chua [Phys. Rev. Lett. 96 （2006） 060502] for teleportation and dense coding with genuine multipartite entanglement, we present an explicit protocol for faithful remote state preparation in a real coefficient case by using the same four-particle entangled state which is not reducible to pair of Bell states. It is shown that any complex coefficient case can be changed to a real coefficient case. With this protocol, the state can play an analogous role to Einstein-Podolsky-Rosen pairs in the theory of multipartite entanglement.     

A genuine four-partite entangled state

In a recent paper, a genuine four-partite entangled state is proposed [Y. Yeo, W.K. Chua, Phys. Rev. Lett. 96 (2006) 060502], which has been found to have many interesting entanglement properties. We show this state is locally equivalent to some graph states.     

Comment on: “Three-party quantum secure direct communication based on GHZ states” [Phys. Lett. A 354 (2006) 67]

The GHZ-state-based quantum secure direct communication (QSDC) protocol [X.-R. Jin, et al., Phys. Lett. A 354 (2006) 67] and its improved version [Z. Man, Y. Xia, Chin. Phys. Lett. 24 (2007) 15] are analyzed from the aspect of security. It shows that much information of the transmitted secret message will be leaked out in both protocols.     

Linear optical implementation of a quantum network for quantum estimation

We present an interferometer for simulating the quantum network for quantum estimation proposed by A.K. Ekert et al. [A.K. Ekert, C.M. Alves, D.K.L. Oi, M. Horodecki, P. Horodecki, L.C. Kwek, Phys. Rev. Lett. 88 (2002) 217901]. We experimentally perform overlap measurements of two single-qubit states with linear optical elements. The scheme is generalized to perform estimation of Trρ³.     

Method for generating a new class of multipartite entangled state in cavity quantum electrodynamics

Recently, Yeo and Chua introduced a genuine four-qubit entangled state |χ〉 which can implement perfect teleportation of an arbitrary two-qubit state [Y. Yeo, W.K. Chua, Phys. Rev. Lett. 96 (2006) 060502]. It has been shown that the state |χ〉 is inequivalent to the well-known Greenberger-Horne-Zeilinger state, W state, and linear cluster state, in terms of stochastic local operations and classical communication [C.F. Wu, Y. Yeo, L.C. Kwek, C.H. Oh, Phys. Rev. A 75 (2007) 032332]. This “new” class of state has many interesting entanglement properties and possible applications in quantum-information processing and fundamental tests of quantum mechanics. Here, we propose a simple scheme to generate the state |χ〉 in cavity quantum electrodynamics. Our idea may be helpful for in-depth study on such a class of state and its practical applications.     

High Efficient Quantum Key Distribution by Random Using Classified Signal Coherent States

The decoy-state method is a useful method in resisting the attacks on quantum key distribution. However, how to choose the intensities of decoy states and the ratio of the decoy states and the signal state is still an open question. We present a simple formula to analyse the problem. We also give a simple method to derive the bounds of the necessary counting rates and quantum bit error rates for BB84 and SARG04; the latter was previously proposed by Scarani et al. [Phys. Rev. Lett. 92 （2004）057901] We then propose a multi-signal-state method which employs different coherent states either as the decoy state or as the signal state to carry out quantum key distribution. We find our protocol more efficient and feasible.     

Sudden death and birth of entanglement beyond the Markovian approximation

We investigate the entanglement dynamics of two initially entangled qubits interacting independently with two uncorrelated reservoirs beyond the Markovian approximation. Quite different from the Markovian reservoirs [C.E. López, et al., Phys. Rev. Lett. 101 (2008) 080503], we find that entanglement sudden birth (ESB) of the two reservoirs occurs without certain symmetry with respect to the entanglement sudden death (ESD) of the two qubits. A phenomenological interpretation of entanglement revival is also given.     

Multi-particle and high-dimension controlled order rearrangement encryption protocols

Based on controlled order rearrange encryption (CORE) for quantum key distribution using EPR pairs [Fu.G. Deng, G.L. Long, Phys. Rev. A 68, 042315 (2003)], we propose generalized controlled order rearrangement encryption (GCORE) protocols of N qubits and N qutrits, and concretely display them in cases using 3-qubit, 2-qutrit maximally entangled basis states. We further show that our protocols will become safer with an increase in dimensions and number of particles. Moreover, we carry out the security analysis using quantum covariant cloning machine. Although the applications of the generalized scheme need to be further studied, GCORE has many distinct features such as large capacity and high efficiency.