Curator's Take
This article shows that the “temporal non‑locality” exhibited by a single qudit is entirely sourced from the purity of its input state rather than any coherence preserved by the channel, overturning the usual intuition that noisy dynamics erode such quantum correlations. By proving a universal bound TNR≤(d–1)/d and linking TNR to a device‑independent lower bound on temporal‑teleportation fidelity, the work provides a new benchmark for assessing time‑forward quantum communication even when the channel is fully decohering. The result also warns that strong temporal‑Bell violations can over‑certify a channel’s actual transmission capability, highlighting the need for careful interpretation of device‑independent metrics in noisy quantum networks.
— Mark Eatherly
Summary
Correlations between two moments in time can be too strong for any classical explanation -- and, remarkably, this can happen for a single quantum system measured twice, with no second particle involved. We show that when one qudit is sent through a noisy channel, the strength of this "nonlocality in time" -- the temporal nonlocality robustness $\mathrm{TNR}$ -- is carried entirely by the starting state: it vanishes precisely when the input is maximally mixed (completely random), $\mathrm{TNR}(ρ_A,\mathcal{E})=0\Leftrightarrowρ_A=\mathbb{1}/d$, for the standard noise families. The resource is not any coherence in the channel but the back-action of the input's mixedness, and it survives even complete decoherence. This is at once a power and a trap. As a power, $\mathrm{TNR}$ device-independently lower-bounds the fidelity of temporal teleportation -- sending an unknown state forward in time -- reaching $7/9$ at $d=3$, without trusting the measuring devices. As a trap, because the certified quantity is decoupled from the channel's actual coherence transmission, it can certify more than the channel delivers: an injective (reversible) unitary attains the maximal temporal-Bell signal yet teleports below the classical baseline. We resolve this over-certification completely -- a universal cap $\mathrm{TNR}\le(d-1)/d$ with an exact channel-resolved value, honest certification for the depolarizing channel and for any sufficiently mixed probe, and a proof that no choice of probes makes it channel-universal. Underpinning the results is a unified semidefinite-programming hierarchy of the temporal entanglement, steering and nonlocality robustnesses ($\mathrm{TER}$, $\mathrm{TSR}$, $\mathrm{TNR}$), with a strict lower hierarchy and an upper one conditional on no-signaling in time ($\mathrm{NSIT}$). All structure is verified numerically for $d=2$ through $5$.