Negative Results on Information-Theoretic Additive Randomized Encodings

Shai Halevi, Yuval Ishai, Eyal Kushilevitz Z +1 more

Çağrı Göken, Sinan Gezici

Estimation theoretic secure transmission of a scalar random parameter is investigated in the presence of an eavesdropper. The aim is to minimize the estimation error at the receiver under a secrecy constraint at the eavesdropper; or, alternatively, to maximize the estimation error at the eavesdropper for a given estimation accuracy limit at the receiver. In the considered setting, the encoder at the transmitter is allowed to use a randomized mapping between two one-to-one and continuous functions and the eavesdropper is fully aware of the encoding strategy at the transmitter. For small numbers of observations, both the eavesdropper and the receiver are modeled to employ linear minimum mean-squared error (LMMSE) estimators, and for large numbers of observations, the expectation of the conditional Cramér-Rao bound (ECRB) metric is employed for both the receiver and the eavesdropper. Optimization problems are formulated and various theoretical results are provided in order to obtain the optimal solutions and to analyze the effects of encoder randomization. In addition, numerical examples are presented to corroborate the theoretical results. It is observed that stochastic encoding can bring significant performance gains for estimation theoretic secrecy problems.

Takayuki Suzuki

Quantum Random Access Codes (QRACs) embody the fundamental trade-off between the compressibility of information into limited quantum resources and the accessibility of that information, serving as a cornerstone of quantum communication and computation. In particular, the $(n, n-1)$-QRACs, which encode $n$ bits of classical information into $n-1$ qubits, provides an ideal theoretical model for verifying quantum advantage in high-dimensional spaces; however, the analytical derivation of optimal codes for general $n$ has remained an open problem. In this paper, we establish an analytical construction method for $(n, n-1)$-QRACs by using an explicit operator formalism. We prove that this construction strictly achieves the numerically conjectured upper bound of the average success probability, $\mathcal{P} = 1/2 + \sqrt{(n-1)/n}/2$, for all $n$. Furthermore, we present a systematic algorithm to decompose the derived optimal POVM into standard quantum gates. Since the resulting decoding circuit consists solely of interactions between adjacent qubits, it can be implemented with a circuit depth of $O(n)$ even under linear connectivity constraints. Additionally, we analyze the high-dimensional limit and demonstrate that while the non-commutativity of measurements is suppressed, an information-theoretic gap of $O(\log n)$ from the Holevo bound inevitably arises for symmetric encoding. This study not only provides a scalable implementation method for high-dimensional quantum information processing but also offers new insights into the mathematical structure at the quantum-classical boundary.

Teiko Heinosaari, Leevi Leppäjärvi, Martin Plávala

Jun Liu, Xiaobin Xu, Quanying Wu +2 more

In this Letter, we propose an information encryption technique based on the theory of phase-space optics. We show that encoding the plaintext in phase space provides a higher level of security: first, the key-space is significantly enlarged. Second, it is immune to various known-plaintext (cyphertext) attacks to which the double-random phase encryption (DRPE) is vulnerable. Third, the bilinearity of phase-space distributions offers additional security. Theoretical analysis and numerical calculation results show that the proposed technique has significantly different responses to errors added to the cypheretext and the two phase keys in comparison to the classical DRPE.

Shinichi Yamada