Abstract Clock interferometry probes general-relativistic proper-time differences through the entanglement between a particle's center-of-mass path and its internal degrees of freedom. Existing analyses treat the internal clock as either a closed system or study how environmental noise modifies the interferometric visibility. Here we address a distinct question: what fraction of the proper-time-induced visibility loss remains recoverable when the experimentalist is restricted to local unitary control of the internal clock? We model the clock as a two-level system undergoing amplitude damping with branch-dependent proper times in a Mach-Zehnder interferometer and derive the visibility both without and with a spin-echo refocusing pulse. In the closed-system limit ($\gamma\to0$), the echo restores full visibility; for $\gamma>0$, the no-jump survival probability imposes a strict upper bound on echo-recovered visibility that no internal-only unitary can exceed. We establish the conditions under which a proper-time-parametrized Gorini-Kossakowski-Sudarshan-Lindblad equation is valid by appealing to the local comoving frame and the equivalence principle, distinguishing comoving-bath and laboratory-bath parametrizations. Numerical simulations with QuTiP confirm all analytic results. We provide experimental parameter estimates for cold-atom and cavity-QED platforms, showing that the irrecoverable visibility deficit is within reach of near-future clock-interferometry experiments. The echo-recovery deficit constitutes an operational witness that separates irreversible environmental decoherence from the formally reversible path-clock entanglement of the Pikovski mechanism.
Abstract Clock interferometry probes general-relativistic proper-time differences through the entanglement between a particle's center-of-mass path and its internal degrees of freedom. Existing analyses treat the internal clock as either a closed system or study how environmental noise modifies the interferometric visibility. Here we address a distinct question: what fraction of the proper-time-induced visibility loss remains recoverable when the experimentalist is restricted to local unitary control of the internal clock? We model the clock as a two-level system undergoing amplitude damping with branch-dependent proper times in a Mach-Zehnder interferometer and derive the visibility both without and with a spin-echo refocusing pulse. In the closed-system limit (γ→0), the echo restores full visibility; for γ>0, the no-jump survival probability imposes a strict upper bound on echo-recovered visibility that no internal-only unitary can exceed. We establish the conditions under which a proper-time-parametrized Gorini-Kossakowski-Sudarshan-Lindblad equation is valid by appealing to the local comoving frame and the equivalence principle, distinguishing comoving-bath and laboratory-bath parametrizations. Numerical simulations with QuTiP confirm all analytic results. We provide experimental parameter estimates for cold-atom and cavity-QED platforms, showing that the irrecoverable visibility deficit is within reach of near-future clock-interferometry experiments. The echo-recovery deficit constitutes an operational witness that separates irreversible environmental decoherence from the formally reversible path-clock entanglement of the Pikovski mechanism.
Quantum clock interferometry makes relativistic proper time enter coherent quantum dynamics through phase and visibility, and within unitary physics the visibility loss from clock-path entanglement is reversible by echo operations. We propose a null test for any residual contrast loss correlated not with the signed proper-time difference but with a non-negative proper-time exposure Ξ. A height-swap echo cancels the signed difference, while keeping Ξ finite. Any residual is parameterized by ln R = − εℓ ω0 Ξ, the law generated by Lindblad dephasing at rate εℓ ω0 |dΔτ/dt|. From published interferometry we derive the first premise-conditioned upper bounds on εℓ: an operational clock-lag reading gives εℓ ≲ 3 × 10−2, while under the contested Compton-frequency reading lattice holds give 1.4 × 10−6 and large-separation fountains give 4 × 10−10. A noise budget shows a dedicated echo with an optical clock is statistics-limited, reaching εℓ ∼ 3 × 10−3within days. Keywords: quantum clocks; quantum interferometry; proper time; gravitational redshift; decoherence; experimental bounds Core claim (operational null test with first bounds). Define the proper-time exposure as Ξ≡ ∫ |dΔτ(t)/dt| dt over the laboratory interval 0 ≤ t ≤ Tlab, and the normalized echo visibility ratio as R(Δh,T) = Vecho(Δh,T)/Vecho(0,T). The null hypothesis is zero slope in ln R versus x= ω0Ξ; any reproducible slope b defines εℓ = −b. Under the assumptions stated in Section 6, an exposure-correlated channel can only reduce contrast, so published visibility data yield conservative upper bounds on εℓ without an echo; the echo is required only for discovery.
Quantum interference of "clocks", namely of particles with time-evolving internal degrees of freedom (DOFs), is a promising avenue to test genuine general relativistic effects in quantum systems. The clock acquires which path information while experiencing different proper times on traversing the arms of the interferometer, leading to a drop in its path visibility. We consider scenarios where the clock is subject to environmental noise as it transits through the interferometer. In particular, we develop a generalized formulation of interferometric visibility affected by noise on the clock. We find that, for small noise and small proper time difference between the arms, the noise further reduces the visibility, while in more general situations it can either increase or reduce the visibility. As an example, we investigate the effect of a thermal environment constituted by a single field mode and show that the visibility drops further as the temperature is increased. Additionally, by considering noise models based on standard quantum channels, we show that interferometric visibility can increase or decrease depending on the type of noise and also the time scale and transition probabilities. The quantification of the effect of noise on the visibility – particularly in the case of a thermal environment paves the way for a better estimate on the expected outcome in an actual experiment.
Optical ion clocks now approach a regime in which relativistic time dilation is no longer exhausted by a classical proper-time parameter read by a quantum sensor. Recent work by Sorci, Foo, Leibfried, Sanner, and Pikovski shows that harmonically trapped optical clock atoms can exhibit vacuum-induced, squeezing-induced, and intrinsically quantum corrections to the second-order Doppler shift, with time-dilation-induced entanglement between motional and internal clock degrees of freedom becoming observable in strongly squeezed trapped-ion motion. This paper develops the significance of that result within CPT-Coherence Theory. The central principle of CPT-Coherence is Onto-Physical Entanglement: what a system is cannot be separated from how it is allowed to remain coherent under admissible transformation. In the clock setting, this principle appears in branch-visible form. The internal clock transition is not merely an isolated label transported through spacetime; its phase identity is dynamically bound to the motional state through the relativistic proper-time operator. Proper-time interferometry therefore supplies a laboratory instance of a more general structural rule: physical identity is stabilized only through the admissible evolution channels by which it can be read out. The paper distinguishes the relativistic proper time of the ion-clock experiment from the coherence-depth coordinate of CPT-Coherence. The former is a branch-visible observable associated with worldline evolution; the latter is a structural coordinate organizing parent-boundary admissibility, trace access, Schur response, and stable observable descent. Their relation is not identity but projection: quantum proper-time readout provides an experimentally precise interface through which branch observers can test how internal identity, motion, coherence, and record formation remain coupled. We formulate a CPT-Coherence clock-readout sector in which a quantum clock is represented by a triple consisting of an internal identity generator, an external motion algebra, and a proper-time readout operator. The Sorci-Foo-Leibfried-Sanner-Pikovski protocol is then interpreted as a high-precision realization of an OPE readout channel: classical time dilation corresponds to scalar proper-time averaging; vacuum and squeezing shifts correspond to state-dependent branch corrections; and visibility loss corresponds to trace-visible entanglement between identity and admissible motion. This establishes optical ion clocks as a natural experimental grammar for CPT-Coherence, while CPT-Coherence supplies a unifying interpretation of why such experiments probe not simply clock rates, but the inseparability of physical being and physical evolution. Scope note: the quantitative predictions below coincide with those of standard relativistic quantum clock theory; CPT-Coherence contributes an interpretation and vocabulary, together with an explicit falsification target for that interpretation.
An operational way of measuring entanglement in a balanced two-path interferometers is presented, where path information is carried by some internal degree of freedom which, in turn, gets entangled with an ancilla system. The analysis is based on a tripartite description involving paths, an internal qubit degree of freedom, and some ancillary states entangled with the internal degree of freedom. It is then applied to two physically distinct experimental situations: a modified Stern-Gerlach interferometer with spin-1/2 particles and a Mach-Zehnder interferometer with photons carrying polarization. The ancilla degree of freedom may not be experimentally accessible. Tracing out the ancillary system, and employing a quantum erasing procedure based on the internal degree of freedom, it is demonstrated that a concurrence-based measure of the entanglement, between the internal degree of freedom and the ancilla, can be extracted directly from measurable asymmetry of the two output channels. These results show that loss of coherence, quantum erasure, and entanglement estimation in interferometric experiments arise from the same underlying correlation structure and provide a compact experimentally accessible framework for quantifying entanglement in qubit systems.
Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter–wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov–Bohm effect, where a particle in a flat space–time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'—a particle with evolving internal degrees of freedom—that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space–time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics. In the theory of general relativity time flows at different rates depending on the space–time geometry. Here, a drop in the visibility of a quantum 'clock' interference in a gravitational potential is predicted, which cannot be explained without the general relativistic notion of time.
We present a unified metric framework describing the loss of spatial interference visibility in relativistic quantum superposition states driven by path-dependent proper-time mismatch. By condensing special-relativistic kinematic time dilation and general-relativistic gravitational redshift into a single, dimensionless differential proper-time rate parameter, ∆τ̇ ≡ |∆Φ/c² − v∆v/c²|, we trace the evolution of spatial trajectories coupled to an internal clock ensemble. Using the reduced density matrix formalism and tracing over internal degrees of freedom, we show that a continuous internal energy dispersion ∆E generates path-discriminating phase information. Evaluating the Fourier transform of a Gaussian spectrum yields an exact, closed-form expression for the spatial coherence envelope decay, defining the characteristic coherence timescale τG = ℏ/(∆E · ∆τ̇). We delineate the physical boundary of this framework: elementary point particles lacking internal energy variance (∆E = 0) experience a deterministic relative phase shift while retaining full quantum contrast, whereas composite systems (∆E > 0) undergo spatial decoherence through relativistically induced path distinguishability. Finally, we demonstrate that expanding the rest-mass phase factor exp(−imc²τ/ℏ) in the weak-field, low-velocity limit naturally yields the time-dependent Schrödinger equation, confirming full compatibility with standard non-relativistic quantum mechanics.