Applications / Experiments read through FDT
Mixed-species network entanglement
Two trapped-ion modules are entangled through photons that meet at a central station, and local logic carries the state onto calcium ions and stores it for more than ten seconds. FDT reads the hosts, the fibres and the motional modes as patterns of one medium: entanglement is a shared density-gradient constraint, settled as one mode of the whole apparatus.
The record
What was measured
Each of two modules, Alice and Bob, holds one 88Sr⁺ ion and one 43Ca⁺ ion in a surface-electrode Paul trap under ultrahigh vacuum, with a bias field of about 0.5 mT setting the quantisation axis. An attempt prepares each strontium ion, excites it with a 10 ps pulse of 422 nm light, and couples the emitted photon into a single-mode fibre. The two fibres meet at a central herald station. Particular detection patterns herald success, and a 674 nm pulse then maps one Zeeman configuration of each strontium ion into its D₅/₂ manifold.
Local mixed-species gates extend the link. An error-detected iSWAP moves the state onto the calcium auxiliary pair, CNOT gates build three- and four-host states, and 402 nm Raman beams map the state into the calcium memory pair. Table I lists the five states characterised.
| Hosts, Alice | Bob | PST (%) | FST (%) | Success, × 10⁻⁴ | Rate (s⁻¹) |
|---|---|---|---|---|
| Sr⁺ | Sr⁺ | 96.0(7) | 96.94(9) | 1.236(3) | 39.31(9) |
| Sr⁺ | Ca⁺ | 95.1(8) | 94.1(6) | 1.03(1) | 7.14(7) |
| Ca⁺ | Ca⁺ | 92(1) | 93.1(7) | 1.24(1) | 8.6(1) |
| Sr⁺ | Sr⁺, Ca⁺ | 94(1) | 93.1(7) | 1.20(1) | 8.26(8) |
| Sr⁺, Ca⁺ | Sr⁺, Ca⁺ | 91(1) | 91.9(8) | 1.44(2) | 9.9(1) |
The fidelity estimator combines a population measurement with a parity scan. For the target family of N hosts, with θ the analyser phase, ϖ the parity phase offset, P the summed all-zero and all-one population and C the parity contrast,
The stored states decay on two very different clocks. The network state’s fitted fidelity-decay constant is 44(3) ms, and its fidelity falls below 50 % beyond 100 ms; the network qubit’s observed coherence time is about 8 ms. The memory holds 69(4) % fidelity at 10 s, with a fitted decay constant of 14(4) s.
The conventional atomic calculation gives each configuration pair’s field slope at the 0.5 mT bias: snet = −11.19 MHz/mT for the network pair, smem = +121.71 kHz/mT for the memory pair and saux = −24.495 MHz/mT for the auxiliary pair. The network pair responds 91.9 times more strongly than the memory pair, and the source attributes the network state’s degradation beyond 10 ms to that sensitivity.
The FDT reading
0.1a Every step a settlement, I-4 the quantum face, P-5 magnetism is geometry
FDT reads the two modules, the fibres and the motional modes as configurations of one medium, the omnium (0.1). The two strontium hosts carry identical closed-pattern constraints, and so do the two calcium hosts; within each module the species differ. Entanglement is the joint density-gradient constraint, settled as one mode of the whole apparatus. Every step is a system-wide settlement (0.1a).
The identity condition sits where the two optical strokes meet, in the herald station. The herald is projection and phase fixation, and the correlation it fixes is a shared bivector grade (I-4): one pattern read at two places, so no signal carries the correlation from Alice to Bob. Read alone, each module’s outcome shares follow no setting of the other module.
Inside a module, the common motional stroke is the local identity constraint. Each CNOT leaves both host gradients in the joint mode, as metronomes on one surface fall into step. There is one carrier and no mediation: the gate is a shared excitation and phase constraint of the one medium (I-2). Gates are events, events do not commute, and a map run back is a second event, never the mirror of the first (0.1a).
The bias field is a macroscopic helical density gradient of the omnium, its axis the quantisation axis (P-5). A qubit frequency compares two configurations of one host inside that gradient, and a response that acts on both alike cancels in their difference (I-3a). The memory pair’s response is 91.9 times smaller than the network pair’s, and the memory holds the mode for seconds where the network pair holds it for milliseconds.
One plate, four views. Run the sequence: after a few attempts the photons herald, and one mode settles across both modules at once while no signal carries the correlation between them; the local gates then bring each calcium ion into step. The other views plot the target-family parity form at unit contrast, the published Table I, and the field slopes with the storage times. The plate is schematic; Table I and the storage values are the published numbers; the slopes are the standard atomic calculation, which rounds to the published −11 MHz/mT and 122 kHz/mT.
0.1a, I-4, P-5
What FDT predicts
Tests the record does not yet contain
P-5 reads an imposed twist, a helix or a rotation as establishing a magnetic field: its axis is the twist axis, and it reverses with the hand. This analysis reads P-5 as fixing the axis and the reversal; P-5 fixes neither an absolute sign nor a magnitude, and both need a declared kernel. Each test is a neighbour comparison whose conventional response cancels, read by the network pair’s free-evolution phase or by a polarimeter, with the bias reversed in interleaved settings and the conventional value stated as the comparator.
- T-1Static torsion outside one module. Place a fused-silica rod outside Alice’s chamber on the bias axis, with the ion beyond one end, and hold equal and opposite static twists while the remote Sr⁺ pair runs in its difference form. FDT reads a residual phase rate odd in the hand, R₁ = snet ΔB₁. A current-free, unmagnetised insulator gives the conventional zero.
- T-2An unstressed helical fibre. Compare left- and right-handed fused-silica coils of one geometry outside one chamber, coaxial with its quantisation axis, with no current flowing. FDT reads a field at the ion that is odd in the hand of the coil. The conventional contrast is zero.
- T-3Nonreciprocal rotation in an asymmetric twisted span. Clamp a fused-silica fibre at one end face and at a point along it, give it equal and opposite twists, and launch weak 422 nm light from each end in turn into a polarimeter. FDT reads a nonreciprocal polarisation rotation odd in the hand: the Faraday rotation of the axial field the twist establishes. The conventional residual is zero after the optical corrections.
- T-4Mechanical rotation beside the trap. Spin a fused-silica disc beside one module about its quantisation axis, at 100 Hz in both senses. FDT reads an axial field odd in the sense of rotation, beyond the four conventional fields: the disc’s Barnett magnetisation, the Rowland and Röntgen fields of its charges, and the drive-current field. Mechanical vorticity and the magnetic moment are two grade projections of one density-gradient topography (P-5).
- T-5Isotope dependence of the glass response. Draw equal single-mode fibres for 422 nm from natural-oxygen silica and from silica with 95 % oxygen-18, and measure each Verdet constant in one calibrated solenoid. At unit density sensitivity FDT reads a logarithmic Verdet ratio of 0.0613 above the consensus comparator, which is bounded by 0.01; the statistical threshold is 0.015 (I-7).
One exploratory exponent describes the two published storage constants in sample: τmem/τnet = |snet/smem|p gives p ≈ 1.27 from the slope ratio of 91.9. It carries no prospective weight, because the decoupling sequence changes with the storage time.
Readings declined
Use 6 Data yes, interpretation not necessarily
Standard reading
The remote state is one joint amplitude of physically separated systems, and its correlations are nonlocal.
FDT reading
The correlation is a shared bivector grade and superposition is ignorance of the helical phase φ₀; the medium’s constrained patterns settle one mode (I-4, 0.1a).
Each ion is a distinct particle with intrinsic properties, and the target is an N-particle GHZ state.
The ions are closed patterns of the one omnium, their masses confinement eigenvalues; the counted entries are hosts of configurations (I-5, 0.1b).
The magnetic field is an independent entity that sets the quantisation axis.
The field is a macroscopic helical density gradient of the omnium, its axis the quantisation axis; a qubit frequency compares two configurations of one host inside it (P-5).
The common motional mode mediates the mixed-species gate.
There is one carrier and no mediation: the gate is a shared excitation and phase constraint of the one medium (I-2).
The Bell-state measurement collapses a joint amplitude and swaps the entanglement onto the ions.
The herald is projection and phase fixation, settled at the common strokes with the full boundary data, never a nonlocal action (I-4, 0.1a).
The gates transfer a quantum state one to one, from one qubit to another.
Each gate or map is a system-wide, many-to-many settlement of the state it starts from, and a map run back is a second event (0.1a, 0.1b).
The vacuum chamber holds an empty background in which c is an abstract constant.
There is no empty background: no variable of the chain vanishes at the chamber’s low pressure, and c² is a property of the omnium (0.1).
Convergence
Use 2 Same source, same data
For the same inputs, the target form, the fitted and reconstructed fidelities of Table I and the exponential storage constants return the consensus states, fringes, fidelities and constants, and the atomic calculation reproduces the source’s rounded slopes of −11 MHz/mT and 122 kHz/mT. That is the identity map of Use 2: the same curvature for the same stress tensor and data (I-3), and the ensemble calculation read on the quantum face of I-4.
FDT departs from general relativity and quantum mechanics here only where it supplies an additional source or a constitutive input: the helical-field source of P-5 in T-1 to T-4, and the density-coupled glass response in T-5. The reconstruction’s own limits carry over unchanged: the fitted storage constants fix no asymptote and no noise spectrum, and the success column gives no common attempt denominator.