The role of entanglement in energy-restricted communication and randomness generation

TL;DR

This work analyzes how entanglement influences energy-restricted prepare-and-measure communication and randomness generation. It develops a general correlation bound for energy-constrained classical channels and shows entanglement does not enhance key classical tasks; for quantum channels, unitary encodings offer no advantage, but non-unitary encoding with higher-dimensional entanglement can unlock significant gains in probabilistic bit transmission and expands the correlator space. The study provides concrete two-qubit and two-qutrit schemes demonstrating these entanglement advantages, and uses both analytical and numerical (SDP) methods to substantiate the results. In randomness generation, the authors show that QRNG security against classical side information largely carries over to low-energy quantum side information, while quantum side information can undermine security at high energy, highlighting a practical incentive to operate in the low-energy regime. Collectively, the results refine the understanding of semi-device-independent quantum information under energy constraints and point to open problems in cryptographic proofs for quantum side information and the universality of entanglement-resourcelessness for energy-restricted classical tasks.

Abstract

A promising platform for semi-device-independent quantum information is prepare-and-measure experiments restricted only by a bound on the energy of the communication. Here, we investigate the role of shared entanglement in such scenarios. For classical communication, we derive a general correlation criterion for nonlocal resources and use it to show that entanglement can fail to be a resource in standard tasks. For quantum communication, we consider the basic primitive for energy-constrained communication, namely the probabilistic transmission of a bit, and show that the advantages of entanglement only can be unlocked by non-unitary encoding schemes that purposefully decohere the entangled state. We also find that these advantages can be increased by using entanglement of higher dimension than qubit. We leverage these insights to investigate the impact of entanglement for quantum random number generation, which is a standard application of these systems but whose security so far only has been established against classical side information. In the low-energy regime, our attacks on the protocol indicate that the security remains largely intact, thereby paving the way for strengthened security without more complex setups and with negligible performance reductions.

Figures (4)

• Figure 1: Entanglement-assisted prepare-and-measure scenario. Alice and Bob share the state $\Psi$. Alice encodes a classical input $x$ into her state, which is assumed to have no more than $\omega$ units of energy, and sends it to Bob. Bob uses his input $y$ to select a measurement whose outcome is outcome $b$.
• Figure 2: Probabilistic bit transmission. Achievable value of $\mathcal{W}_2$ at energy at most $\omega$ for quantum messages without entanglement (blue), with two-qubit entanglement (green) and with two-qutrit entanglement (red).
• Figure 3: Achievable correlators in quantum models. The use of entanglement enlarges the space of achievable correlator pairs as compared to the quantum region (blue) reported in VanHimbeeck2017. Illustration for $\omega=0.2$.
• Figure 4: Randomness certification and quantification of quantum side information attacks. Adversaries with access to pre-shared entanglement with the preparation and measurement devices can harness the correlations that arise in energy-restricted EAPM scenarios to violate lower-bounds on the randomness certified considering classical side information. The impact of these attacks grows in high-energy regimes, but remains negligible at low energies.