Covert Entanglement Generation and Secrecy

TL;DR

The paper determines the covert capacity for entanglement generation over noisy quantum channels and shows a square-root scaling, enabling about ${\sqrt{n}}$ EPR pairs to be generated covertly in $n$ channel uses. It constructs covert secrecy codes for classical information, then leverages Devetak’s method to transform these into entanglement-generation codes, yielding a single-letter capacity $C_{EG}(\mathcal{N})=\frac{D(\sigma_1||\sigma_0)}{\sqrt{\tfrac{1}{2}\chi^2(\omega_1||\omega_0)}}$ under standard support conditions. The results demonstrate that the same covert rate as classical information applies to entanglement generation, albeit with a larger secret key, and they provide explicit channel examples (generalized dephasing and excitation channels) to illustrate the capacity expressions. The work integrates covert communication, secrecy, and decoupling techniques, highlighting a fundamental link between secrecy and entanglement generation in quantum networks with an adversarial warden. It also discusses practical implications and directions for extending to broader quantum-channel models and infinite-dimensional settings.

Abstract

We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission itself remains undetectable. The entanglement dimension follows a square root law (SRL) in the covert setting, i.e., $O(\sqrt{n})$ EPR pairs can be distributed covertly and reliably over n channel uses. We begin with covert communication of classical information under a secrecy constraint. We then leverage this result to construct a coding scheme for covert entanglement generation. Consequently, we establish achievability of the same covert entanglement generation rate as the classical information rate without secrecy, albeit with a larger key.

Figures (4)

• Figure 1: Covert entanglement generation. Alice prepares a maximally entangled state $\ket{\Phi}_{RM}$, locally, where $R$ is a resource that she keeps, and $M$ is the resource that she would like to distribute to Bob. Alice makes a decision on whether to perform the communication task, or not. If Alice decides to be inactive, the channel input is $\ket{0}^{\otimes n}$. Otherwise, she applies an encoding map to prepare the channel input $A^n$ using a pre-shared secret key. She then transmits $A^n$ via the quantum channel $\mathcal{U}_{A\rightarrow BW}^{\otimes n}$. Bob receives $B^n$, and uses the key to perform a decoding operation and prepare ${\widehat{M}}$ such that Alice and Bob's state is $\approx \ket{\Phi}_{R\widehat{M}}$. Willie would like to detect the transmission. To this end, he performs a hypothesis-test measurement on his output $W^n$ to estimate whether Alice is quiet (null hypothesis $H_0$) or transmitting (alternate hypothesis $H_1$).
• Figure 2: Covert secrecy for a classical-quantum channel. Suppose Alice selects a classical message $m$. She makes a decision on whether to send it to Bob, or be inactive, in which case the channel input is $x^n=0^n$. Otherwise, she encodes her message $m$ using her access to the pre-shared secret and transmits a codeword $x^n=f{(m,k)}$ via $\mathcal{P}_{X\rightarrow BW}^{\otimes n}$. At the channel output, Bob uses the key and performs a decoding measurement on his received system $B^n$, and obtains an estimate $\hat{m}$. Willie attempts to detect and decode Alice's transmission and message by measuring his received system $W^n$.
• Figure 3: Covert entanglement-generation capacity of a generalized dephasing channel as a function of parameter $p$.
• Figure 4: Covert entanglement-generation capacity of an excitation channel as a function of excitation probability $\gamma$.

Theorems & Definitions (38)

• Remark 1
• Definition 1
• Definition 2: Achievable covert secrecy rate
• Definition 3: Covert secrecy capacity
• Theorem 1
• Remark 2
• Remark 3
• Remark 4
• Definition 4
• Remark 5