Fault tolerant quantum dialogue protocol over a collective noise channel

In this paper, two information leakage resistant quantum dialogue (QD) protocols over a collective-noise channel are proposed. Decoherence-free subspace (DFS) is used to erase the influence from two kinds of collective noise, i.e., collective-dephasing noise and collective-rotation noise, where each logical qubit is composed of two physical qubits and free from noise. In each of the two proposed protocols, the secret messages are encoded on the initial logical qubits via two composite unitary operations. Moreover, the single-photon measurements rather than the Bell-state measurements or the more complicated measurements are needed for decoding, making the two proposed protocols easier to implement. The initial state of each logical qubit is privately shared between the two authenticated users through the direct transmission of its auxiliary counterpart. Consequently, the information leakage problem is avoided in the two proposed protocols. Moreover, the detailed security analysis also shows that Eve's several famous active attacks can be effectively overcome, such as the Trojan horse attack, the intercept-resend attack, the measure-resend attack, the entangle-measure attack and the correlation-elicitation (CE) attack.

Using three-photon polarization-entangled GHZ states or W states, we propose controlled quantum key distribution protocols for circumventing two main types of collective noise, collective dephasing noise, or collective rotation noise. Irrespective of the number of controllers, a three-photon state can generate a one-bit secret key. The storage technique of quantum states is dispensable for the controller and the receiver, and it therefore allows performing the process in a more convenient mode. If the photon cost in a security check is disregarded, then the efficiency theoretically approaches unity.

In this paper, using the quantum entanglement swapping technologies under the collective-dephasing noise and the collective-rotation noise, two robust quantum dialogue protocols are proposed, respectively. The logical Bell states are used as the traveling states to combat the collective noise. The auxiliary logical Bell state is shared privately between two participants through the manner of direct transmission first. After encoded with the receiver's secret messages, it swaps entanglement with its adjacent logical Bell state. In this way, the information leakage problem is avoided. Moreover, Eve's active attacks can be detected with the help of decoy photon technology. For decoding, the Bell state measurements rather than the four-qubit joint measurements are needed.

The collective noises, which include the collective-dephasing noise and the collective-rotation noise, are the topical noises in quantum key agreement (QKA). How to eliminate the influence of the collective noises on quantum communication is a problem to be solved urgently. In this paper, based on logical quantum states, by using controlled-Z, controlled-NOT and unitary operations, two QKA protocols which can be immune to the collective-dephasing noise and the collective-rotation noise are proposed, respectively. The security analysis indicates that these two protocols can resist participant attack and outsider attacks which include Trojan-horse attacks, intercept-resend attack, measure-resend attack and entangle-measure attack. By comparing with the proposed two-party QKA protocols against the collective noises, it is clear that our protocols are more efficient.

We present a faithful qubit transmission scheme with linear optics against collective noise, not resorting to ancillary qubits. Its setup is composed of three unbalanced polarization interferometers, based on a polarizing beam splitter, a beam splitter, and a half wave plate, which makes this scheme more feasible than others with present technology. The fidelity of successful transmission is 1, independent of the parameters of the collective noise, and the success probability for obtaining an uncorrupted state can be improved to 100% with some time delayers. Moreover, this scheme has some good applications in one-way quantum communication for rejecting the errors caused by the collective noise in quantum channel.

In general, implementing a multi-logical-qubit gate by manipulating quantum states in a decoherence-free subspace (DFS) becomes more complex and difficult when increasing the number of logical qubits. In this work, we propose an idea to realize quantum gates by manipulating quantum states outside their DFS but having the states of the logical qubits remain in their DFS before and after the gate operation. This proposal has the following features: (i) because the states are manipulated outside the DFS, the multiqubit gate implementation can be simplified when compared to realizing a multiqubit gate via manipulating quantum states within the DFS, which usually requires unitary operations over a large DFS, and (ii) because the states of the logical qubits return to the DFS after the gate operation, the errors caused by decoherence during the gate operation are not accumulated for a long-running calculation, and the states of the logical qubits are immune to decoherence when they are stored. Based on this proposal, we then present a way for realizing a multi-target-qubit controlled-not gate using logical qubits encoded in a decoherence-free subspace against collective dephasing. This gate is realized by employing qutrits (three-level quantum systems) placed in a cavity or coupled to a resonator. This proposal has the following advantages: (i) the states of the logical qubits return to their DFS after the gate operation; (ii) the gate can be implemented with only a few basic operations; (iii) the gate operation time is independent of the number of logical qubits; (iv) this gate can be deterministically implemented because no measurement is needed; (v) the intermediate higher-energy level for all qutrits is not occupied during the entire operation, thus decoherence from this level is greatly suppressed; (vi) this proposal is universal and can be applied to realize the proposed gate using natural atoms or artificial atoms (e.g., quantum dots, nitrogen-vacancy centers, and various superconducting qutrits, etc.) placed in a cavity or coupled to a resonator. As an application, we also show how to apply this gate to create a Greenberger-Horne-Zeilinger (GHZ) entangled state of multiple logical qubits encoded in DFS, and further investigate the experimental feasibility for creating the GHZ state of three logical qubits in the DFS, by using six superconducting transmon qutrits coupled to a one-dimensional coplanar waveguide resonator.

Quantum digital signature (QDS) has been proved to be secure in theory, but will inevitably be interfered by channel noise during the practice transmission of qubits. We propose two practical fault tolerant quantum digital signature protocols for the collective noises. For resisting the collective noises, a decoherence-free subspace (DFS) containing four logical qubits has been constructed, which improves the performance of QDS protocols in terms of communication fidelity. Moreover, we prove that the protocols are secure against forging and repudiation attacks, and further discuss the influence of different verification thresholds on the security and give a quantitative analysis.

Very recently, Yin and Tang proposed a two-step efficient quantum dialogue (QD) protocol with three-particle entangled W state (Yin and Tang Int. J. Theor. Phys. 53, 2760 2014). In this Letter, the security loophole named information leakage, i.e., anybody else can elicit partial information of secret messages without any active attack, is discovered and deduced in detail. Furthermore, the essence of information leakage is studied from the viewpoint of Holevo theorem.

This work proposes controlled quantum secure direct communication (CQSDC) over an ideal channel. Based on the proposed CQSDC, two fault-tolerant CQSDC protocols that are robust under two kinds of collective noises, collective-dephasing noise and collective-rotation noise, respectively, are constructed. Due to the use of quantum entanglement of the Bell state (or logical Bell state) as well as dense coding, the proposed protocols provide easier implementation as well as better qubit efficiency than other CQSDC protocols. Furthermore, the proposed protocols are also free from correlation-elicitation attack and other well-known attacks.

We have proposed two deterministic remote state preparation schemes via the χ state as the entangled channel in ideal environment. In this paper, we re-investigate the schemes in seven types of noises: amplitude-damping, phase-damping, Pauli (bit-flip, phase-flip, bit-phase flip, depolaring) and collective dephasing noise. The fidelity is used to measure how close the output state with the initial state are. It is found that the fidelities are dependent on the amplitude factor, phase factor and noise parameter. Interestingly, the fidelity is irrelated to the participators’ measurement results except in the amplitude-damping and collective dephasing noise. When the prepared states are the specific two- and three-qubit states, the fidelity is periodic in the collective dephasing noise and monotonous in other noises. Moreover, the average fidelity and state-independent average fidelity are calculated to quantify the effect of noise. Among the amplitude-damping, phase-damping and Pauli noises, the Pauli noise has the greatest impact and the phase-damping noise has the smallest impact.

The multiple-qubit logical basis, originally introduced in the context of fault-tolerant quantum computing in decoherence-free subspace (DFS), has specific applications for resolving a reference frame misalignment problem in quantum information protocols. In this paper, an alignment-free MDI-QKD scheme is proposed with rotational-invariant state, which is immune to the collective noise induced by misalignment between two distant legitimate parties. In our protocol, the initial logical qubit is created in the polarization-orbit angular momentum hybrid space, while the transmission is entirely done in the rotation-invariant DFS under the collective noise associated with misalignment. The partial Bell state measurement is performed on the logical qubits to sort the logical Bell state. Compared with the original MDI-QKD protocols, the numerical simulations show that our modified scheme has apparent improvements both in transmission distance and key generation rate. Furthermore, only ordinary optical elements are required in our protocol.

Security of the quantum secure direct communication protocol (i.e., the C-S QSDC protocol) recently proposed by Cao and Song [Chin. Phys. Lett. 23 (2006) 290] is analyzed in the case of considerable quantum channel noise. The eavesdropping scheme is presented, which reveals that the C-S QSDC protocol is not secure if the quantum bit error rate (QBER) caused by quantum channel noise is higher than 4.17%. Our eavesdropping scheme induces about 4.17% QBER for those check qubits. However, such QBER can be hidden in the counterpart induced by the noisy quantum channel if the eavesdropper Eve replaces the original noisy channel by an ideal one. Furthermore, if the QBER induced by quantum channel noise is lower than 4.17%, then in the eavesdropping scheme Eve still can eavesdrop part of the secret messages by safely attacking a fraction of the transmitted qubits. Finally, an improvement on the C-S QSDC protocol is put forward.

Quantum computing in decoherence-free subspaces with coupled charge qubits

Deterministic secure quantum communication against collective noise

In this paper, we present a scheme for quantum dialogue by using a four-qubit cluster state as quantum channel.The scheme has two cases: Case 1, Sender Alice and receiver Bob share information using an orderly sequence of entangled state as quantum channel which was prepared by Alice. This case is achieved as follows: The two sides agreed to encode quantum state information, then Alice perform a bell state measurement for quantum information which has been encoded. This will convey the information to Bob, then Bob measuring his own qubits, through the analysis of the measurement results of Alice and Bob, Bob can obtain quantum information. For case 2, four-qubit cluster state and quantum state information is transmitted to form a total quantum system. In the Case 2 scenario, Alice and Bob perform bell state measurements for part of the qubits, and tell the measurement result to each other through the classical channel. Finally, according to the measurement result, Alice and Bob operate an appropriate unitary transformation, as a result, Alice’s qubit will be renewed upon Bob’s measurements, and also, Bob’s qubit will be renewed upon Alice’s measurements. Thus, a bidirectional quantum dialogue is achieved. After analysis, this scheme has high security by taking certain eavesdropping attacks into account. There is therefore a certain reference value to the realization of quantum dialogue.