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arXiv:2607.02331

Temporal nonlocality of a qudit resides in the input state, not the channel, and certifies temporal teleportation up to a fundamental limit

Karol Bartkiewicz, Patrycja Tulewicz

quant-phSubmitted Jul 2, 2026• Announced Jul 3, 2026• 0 citations
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Abstract

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 $5$.

Comments
21 pages, 4 figures; supplementary material 12 pages, 5 figures. Comments welcome

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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 TNR\mathrm{TNR}TNR -- is carried entirely by the starting state: it vanishes precisely when the input is maximally mixed (completely random), TNR(ρA,E)=0⇔ρA=1/d\mathrm{TNR}(ρ_A,\mathcal{E})=0\Leftrightarrowρ_A=\mathbb{1}/dTNR(ρA​,E)=0⇔ρA​=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, TNR\mathrm{TNR}TNR device-independently lower-bounds the fidelity of temporal teleportation -- sending an unknown state forward in time -- reaching 7/97/97/9 at d=3d=3d=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 TNR≤(d−1)/d\mathrm{TNR}\le(d-1)/dTNR≤(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 (TER\mathrm{TER}TER, TSR\mathrm{TSR}TSR, TNR\mathrm{TNR}TNR), with a strict lower hierarchy and an upper one conditional on no-signaling in time (NSIT\mathrm{NSIT}NSIT). All structure is verified numerically for d=2d=2d=2 through 555.
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Quantum teleportation, a cornerstone of quantum information science, enables the transfer of an unknown quantum state from one location to another without physically moving the particle itself. Its fidelity is paramount for practical applications in quantum computing and secure communication. A fundamental principle underpinning quantum mechanics is the no-cloning theorem, which prohibits the creation of an identical copy of an arbitrary unknown quantum state. This paper proposes and theoretically investigates a novel protocol for enhancing the fidelity of quantum teleportation by incorporating Bell-certified unclonability. By leveraging the strong correlations inherent in maximally entangled Bell states, our scheme introduces a mechanism to verify that the quantum state being teleported has not been illicitly copied prior to or during the teleportation process. This certification is achieved through local measurements and Bell tests, which confirm the integrity of the entangled channel and, by extension, the unclonability of the transmitted state. We analyze the theoretical underpinnings of this Bell-certification, its impact on the average fidelity of teleported states, and its robustness against various noise models. Our findings demonstrate that integrating unclonability certification through Bell tests significantly bolsters the security and reliability of quantum teleportation, offering a pathway towards truly high-fidelity and secure quantum information transfer in realistic noisy environments.
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