Quantum information and reversible computation: SMM/DTT and relational quantum mechanics

01The question behind this comparison

Quantum information is encoded in states and transformations whose coherence matters to the result. A reversible computation acts bijectively on the relevant state space; a quantum circuit ordinarily uses unitary gates. Irreversible operations such as resetting a register require an environment or another information-bearing resource. A source can carry out a long sequence of reversible inner steps while releasing an effectively irreversible record at its outer interface.

This makes DTT a promising language for separating work, memory and publication. Its distinct ambition is to connect those computational roles to the production of physical structure itself. A simulation of particles on a pre-existing lattice is not yet an explanation of why space exists. The key mathematical question is which architecture and resource restrictions force an observable geometry or clock relation, rather than merely allow an arbitrary controller to implement one. ^{[3] [4]}

02The SMM/DTT starting point

The Single Monad Model begins with one nonspatial generative source. The Duality of Time Theory distinguishes the source’s inner production from the outer order in which completed records become accessible. Its six inner levels are nested functional roles of one process: a higher role organizes lower-level work. The seventh is the completion or observation interface. They are neither six independent clocks nor six additional time coordinates.

This distinction supplies a useful research question: which features of an observed world can follow from the way a source produces, retains and releases information? A concrete answer needs a state space, an autonomous update, retained memory and a rule connecting completion to an accessible measurement. In the constructions discussed here, those mathematical ingredients are stated explicitly. A successful finite example establishes what its specified mechanism can do; further arguments connect it to physical particles, spacetime or universal laws. ^[1]

03How the comparator works

Relational quantum mechanics treats physical quantities and state assignments as relative to interactions between systems. An observer is any relevant physical system, not necessarily a conscious mind. What is definite relative to one system need not be represented by the same state relative to an external system that has not yet interacted with it. Communication and subsequent interactions are part of the physical account of how records are compared.

DTT’s separation of generation from accessible records can be formulated in this language when completion is indexed to a receiving system. A universal outer archive, by contrast, would add an observer-independent structure beyond Rovelli’s original proposal. Neither choice is settled merely by saying that observations occur. The useful comparison concerns exactly which system retains a record, which interactions make it accessible, and which consistency conditions connect descriptions. Relational quantum mechanics does not derive the six inner levels, while their presence alone does not decide whether completion should be universal or relational. ^[2]

04The decisive comparison

Relational quantum mechanics describes a computational output as a record established through interactions between the processor, memory and reader. A coherent process can remain available relative to a larger controlled system while a smaller receiver has already registered a classical label. DTT’s completion interface can model this organization if its notion of completion includes who receives the record and which later operations remain physically possible.

The no-cloning theorem clarifies why such access matters. Two recipients can share copies of an orthogonal output label without each possessing an independent copy of the processor’s unknown quantum state. A source archive may therefore support agreement among observers while retaining a more restricted coherent resource. DTT could contribute a derived rule governing this distribution and its cost. An absolute universal archive, however, would add structure beyond the relational interpretation and would need its own causal-access account. The six inner roles can organize a computational implementation, but their presence does not establish a universal architecture. A physical selection principle must explain why the source uses those roles and why its permitted receivers see the resulting information limits. ^{[2] [3] [4]}

05Worked benchmark

Suppose a unitary device could copy every unknown qubit: U|ψ⟩|0⟩=|ψ⟩|ψ⟩. Apply it to two possible inputs |ψ⟩ and |φ⟩. Unitarity preserves their inner product, so s=⟨ψ|φ⟩ must satisfy s=s². This requires s=0 or s=1. Two distinct nonorthogonal states, such as |0⟩ and |+⟩ with s=1/√2, cannot both be copied perfectly by that device.

The result still permits copying an orthogonal classical record. A controlled-NOT gate sends |0⟩|0⟩ to |0⟩|0⟩ and |1⟩|0⟩ to |1⟩|1⟩. On a superposition it creates entanglement rather than two independent copies. Thus an outer archive may distribute a stable outcome label widely without cloning the full inner quantum state. This simple distinction prevents the cosmic-computer analogy from assuming an impossible universal backup of unknown quantum information. ^{[3] [4]}

06What follows for the source programme

A source-based computational model becomes informative when it includes the cost of protected memory, resetting and local access. Quantum error correction shows that reliable logical information can survive selected errors through redundancy without cloning an unknown state. DTT can investigate whether the same protection rules also select completed records or effective neighborhoods. That is a more concrete route than identifying the cosmos with a computer solely because its history can be represented as a sequence of symbols. ^{[3] [4]}

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

Continue on SMONAD

• The Cosmic Computer →

  Connects this comparison with the author’s underlying construction.

• A quantum source for generation and completion →

  Connects this comparison with the author’s underlying construction.

• Undoing rejected partial work →

  Connects this comparison with the author’s underlying construction.

• From a continuous pointer to a binary memory →

  Connects this comparison with the author’s underlying construction.

• SMM/DTT research claim map: results, assumptions and open targets →

  Places the comparison alongside the programme’s published results, assumptions and open targets.