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arXiv:1405.0943 · International Journal of Quantum Information

Encoding secret information in measurement settings

Syed M. Assad, Amir Kalev

Published Apr 1, 2014• 1 citation
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Abstract

Secure communication protocols are often formulated in a paradigm where the message is encoded in measurement outcomes. In this work, we propose a rather unexplored framework in which the message is encoded in measurement settings rather than in their outcomes. In particular, we study two different variants of such secure communication protocols in which the message alphabet corresponds to measurement settings of mutually unbiased bases.

DOI
10.1142/s0219749914500166

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Secure communication protocols are often formulated in a paradigm where the message is encoded in measurement outcomes. In this work, we propose a rather unexplored framework in which the message is encoded in measurement settings rather than in their outcomes. In particular, we study two different variants of such secure communication protocols in which the message alphabet corresponds to measurement settings of mutually unbiased bases.
Mutually unbiased bases (MUBs) are a crucial ingredient for many protocols in quantum information processing. Measurements performed in these bases are unbiased to the maximally possible extent, which is used to prove the randomness or secrecy of measurement results. In this work we show that certain properties of sets of MUBs crucially depend on their specific choice, including, somewhat surprisingly, measurement outcome labeling. If measurements are chosen in a coherent way, the secrecy of the result can be completely lost for specific sets of MUB measurements but partially retained for others. This could potentially impact a broad spectrum of applications where MUBs are utilized.
It has been found that the signal can be encoded in the choice of the measurement basis of one of the communicating parties, while the outcomes of the measurement are irrelevant for the communication and therefore may be discarded. The proposed protocol was novel and interesting, but it wasn't secure for communication. The eavesdropper can obtain the information without being detected. We utilize the outcomes of the measurement to propose a secure communication protocol. And the error correction code is used to increase the fault tolerance in the noise.
Orbital angular momentum (OAM) states of photons span a high-dimensional Hilbert space, and by using it, higher information capacity and enhanced security can be achieved for both classical communication and quantum key distribution. In this work, we propose a feasible basis-independent encoding scheme for OAM states and show its application in high-dimensional quantum secure direct communication, which enables direct transmission of meaningful messages, in addition to random secret key establishing. Imperfections of optical components may reduce the efficiency of the encoding scheme and, thus, the channel capacity. We discuss the optimal input distribution under realistic conditions to achieve maximal mutual information and an alternative solution using a different set of mutually unbiased bases in the case of a prime-dimensional quantum system.
Recently, Kalev et al. [A. Kalev, A. Mann, and M. Revzen, Phys. Rev. Lett. 110, 260502 (2013).] proposed a quantum (public) communication protocol with an interesting encoding style, where the signal is encoded in the choice of the measurement basis of one of the communicating parties (Bob) and Bob's measurement results are irrelevant for the communication. As we know, one of the main advantages of quantum technique in communication over the classical one is the higher security. Therefore, as Kalev et al. have mentioned in their paper, an interesting open question is whether one could and how to utilize this new encoding style to design a secure communication protocol, i.e., translate the choice of measurement into the secret. Here we propose a quantum key distribution protocol, which is a secure communication protocol, with this encoding style, where Bob's measurement results are still irrelevant. Furthermore, the security of the proposed protocol in the zero-error case has been proved.
We propose two schemes for realizing quantum secure direct communication (QSDC) by using a set of ordered two-photon three-dimensional hyperentangled states entangled in two degrees of freedom (DOFs) as quantum information channels. In the first scheme, the photons from Bob to Alice are transmitted only once. After insuring the security of the quantum channels, Bob encodes the secret message on his photons. Then Alice performs single-photon two-DOF Bell bases measurements on her photons. This scheme has better security than former QSDC protocols. In the second scheme, Bob transmits photons to Alice twice. After insuring the security of the quantum channels, Bob encodes the secret message on his photons. Then Alice performs two-photon Bell bases measurements on each DOF. The scheme has more information capacity than former QSDC protocols.