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Theoretical and Applied Informatics

Security of the quantum direct communication based on pairs of completely entangled qudits

Piotr Zawadzki

Published Jan 1, 2011• 0 citations
Publisher

Abstract

Quantum secure direct communication protocols offer confidential transmission of classic information over the quantum channel without a prior key agreement. The ping-pong based protocols provide asymptotic security and detailed analysis of the security level provided by each variant of the protocol is required. The paper presents a general method of calculation of the eavesdropped information as a function of the attack detection probability. The method is applied to the ping-pong protocol based on completely entangled pairs of qudits. The lower and upper bound on the amount of the leaked information is provided.

DOI
10.2478/v10179-011-0006-8

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Quantum secure direct communication protocols offer confidential transmission of classic information over the quantum channel without a prior key agreement. The ping-pong based protocols provide asymptotic security and detailed analysis of the security level provided by each variant of the protocol is required. The paper presents a general method of calculation of the eavesdropped information as a function of the attack detection probability. The method is applied to the ping-pong protocol based on completely entangled pairs of qudits. The lower and upper bound on the amount of the leaked information is provided.
Quantum secure direct communication protocols offer confidential transmission of classic information over quantum channel without prior key agreement. The ping-pong based protocols provide asymptotic security and detailed analysis of security level provided by each variant of the protocol is required. The paper presents a general method of calculation of the eavesdropped information as a function of the attack detection probability. The method is applied to the ping-pong protocol based on completely entangled pairs of qudits. The upper and lower bounds on the amount of the leaked information and eavesdropping detection probability are provided.
A novel secure communication protocol is presented, based on an entangled pair of qubits and allowing asymptotically secure key distribution and quasi-secure direct communication. Since the information is transferred in a deterministic manner, no qubits have to be discarded. The transmission of information is instantaneous, i.e. the information can be decoded during the transmission. The security against arbitrary eavesdropping attacks is provided. In case of eavesdropping attacks with full information gain, the detection rate is 50% per control transmission. The experimental realization of the protocol is feasible with relatively small effort, which also makes commercial applications conceivable.
A new quantum secret sharing protocol based on the ping-pong protocol of quantum secure direct communication is proposed. The pairs of entangled qutrits are used in protocol, which allows an increase in the information capacity compared with protocols based on entangled qubits. The detection of channel eavesdropping used in the protocol is being implemented in random moments of time, thereby it is possible do not use the significant amount of quantum memory. The security of the proposed protocol to attacks is considered. A method for additional amplification of the security to an eavesdropping attack in communication channels for the developed protocol is proposed.
A quantum secure direct communication (QSDC) protocol based on the hyper-entangled state is proposed to improve the efficiency of eavesdropping detection in an improved “ping-pong” protocol, in which we use the hyper-entangled state to detect eavesdropping during the quantum communication. In the security analysis, we use the entropy theory method to calculate the amount of information and compare the detection strategy of two QSDC protocols quantitatively by comparing the constraint between the maximal amount of information that the eavesdropper can get, and the probability that the eavesdropper is detected. The probability of being detected will be 50% in the original QSDC protocol which based on the Bell states if the eavesdropper attempts to get all the information, however, in the proposed protocol this probability can reach 75%, which indicates that the proposed protocol is more secure.
In this paper the analyses of the eavesdropping attack of two or more eavesdroppers on the original ping-pong protocol with entangled pairs of qubits is carried out. General recursive expression for probability d of attack detection for any number n of eavesdroppers that allows to calculate this probability through the corresponding probability when n – 1 eavesdroppers attack is obtained. It is shown that an increase in the number of attackers in the quantum channel leads to an increase in the probability of detecting these attacks by legitimate users. The expressions for the maximum eavesdroppers' amount of information during a consistent attack of two and three eavesdroppers are obtained. It is indicated that the maximum eavesdroppers' amount of information determined by the same expression as in the case of one eavesdropper's attack, only the value of d is varying. It is shown that the ping-pong protocol with pairs of entangled qubits is vulnerable to eavesdropping attack of several eavesdroppers not more than to one eavesdropper's attack.
Quantum direct communication (QDC) can bring confidentiality of sensitive information without any encryption. A ping-pong protocol, a well-known example of entanglement-based QDC, offers asymptotic security in a perfect quantum channel. However, it has been shown (Wójcik in Phys Rev Lett 90(15):157901, 2003. doi: 10.1103/PhysRevLett.90.157901 ) that it is not secure in the presence of losses. Moreover, legitimate parities cannot rely on dense information coding due to possible undetectable eavesdropping even in the perfect setting (Pavičić in Phys Rev A 87(4):042326, 2013. doi: 10.1103/PhysRevA.87.042326 ). We have identified the source of the above-mentioned weaknesses in the incomplete check of the EPR pair coherence. We propose an improved version of the control mode, and we discuss its relation to the already-known attacks that undermine the QDC security. It follows that the new control mode detects these attacks with high probability and independently on a quantum channel type. As a result, an asymptotic security of the QDC communication can be maintained for imperfect quantum channels, also in the regime of dense information coding.