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In reply to Vaidmans Comment [arXiv:1304.6689], we show that his claim that our Protocol for Direct Counterfactual Quantum Communication [PRL 110, 170502 (2013), arXiv:1206.2042] is counterfactual only for one type of information bit is wrong.
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In this Reply we propose a modified security proof of the Quantum Dense Key Distribution protocol detecting also the eavesdropping attack proposed by Wojcik in his Comment.
In [J.S. Shaari, M. Lucamarini, M.R.B. Wahiddin, Phys. Lett. A 358 (2006) 85-90] the deterministic six states protocol (6DP) for quantum communication has been developed. This protocol is based on three mutually unbiased bases and four encoding operators. Information is transmitted between the users via two qubits from different bases. Three attacks have been studied; namely intercept-resend attack (IRA), double-CNOT attack (2CNOTA) and quantum man-in-the-middle attack. In this Letter, we show that the IRA and 2CNOTA are not properly addressed. For instance, we show that the probability of detecting Eve in the control mode of the IRA is 70% instead of 50% in the previous study. Moreover, in the 2CNOTA, Eve can only obtain 50% of the data not all of it as argued earlier.
We stand by our findings in Phys. Rev A. 96, 022126 (2017). In addition to refuting the invalid objections raised by Peleg and Vaidman, we report a retrocausation problem inherent in Vaidmans definition of the past of a quantum particle.
A corresponding comment, raised by Kao and Hwang, claims that the reconstructor Bob1 is unable to obtain the expected secret information in (t, n) Threshold d-level Quantum Secret Sharing (TDQSS)[Scientific Reports, Vol. 7, No. 1 (2017), pp.6366] . In this reply, we show the TDQSS scheme can obtain the dealers secret information in the condition of adding a step on disentanglement.
The above comment [E. I. Lashin, D. Dou, arXiv:1606.04738] claims that the paper Quantum Raychaudhuri Equation by S. Das, Phys. Rev. D89 (2014) 084068 [arXiv:1404.3093] has problematic points with regards to its derivation and implications. We show below that the above claim is incorrect, and that there are no problems with results of the above paper or its implications.
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