Answer · confidence: partial
Do science books say sealed notes only go one way? What would change that?
Research question: Do physics textbooks treat a sealed message as a strictly one-way channel, and what would have to change for a two-way loop with a reply to be possible?
The verified facts do not address what physics textbooks say about sealed messages, so the textbook part of the question cannot be answered directly 11. The records show that the no-communication theorem holds that one observer cannot transmit information through measurement of an entangled state, provided neither observer affects the preparation of the initial state 67. Bit commitment is described as a one-way handover, and unconditionally secure bit commitment is forbidden by quantum mechanics 2120. A two-way loop with a reply would need a closed timelike curve, a worldline that returns a signal to its own past, which general relativity permits as a hypothetical construct 131417. The newest supporting facts date from 2026, so this material is current within the year 1417.
Checked 2026-10-22. Only documented and supported facts are used.
Dig deeper on this questionSources
[1] documented
The no-cloning theorem is fundamentally linked to the concept that a single quantum state cannot be copied, which restricts information transmission.
"W. K. Wootters and W. H. Zurek: A single quantum cannot be cloned. Nature 299, 802–803 (1982)"No-Cloning Theorem (2009)
[2] supported
The no-cloning theorem has implications for communication using EPR devices, suggesting constraints on how quantum information can be transmitted or shared.
"D. Dieks: Communication by EPR devices. Phys. Lett. A 92, 271 (1982) 271–272"No-Cloning Theorem (2009)
[3] documented
Noncommuting mixed states cannot be broadcast, which is a generalization of the no-cloning principle affecting how quantum information can be distributed.
"H. Barnum, C. Caves, C. Fuchs, R. Jozsa, and B. Schumacher: Noncommuting mixed states cannot be broadcast. Phys. Rev. Lett. 76, 2818–2821 (1996)"No-Cloning Theorem (2009)
[4] documented
There are concepts of quantum copying that go beyond the strict no-cloning theorem, implying that approximate or probabilistic cloning might be possible under certain conditions.
"V. Bužek and M. Hillery: Quantum copying: Beyond the no-cloning theorem. Phys. Rev. A 54, 1844–1852 (1996)"No-Cloning Theorem (2009)
[5] supported
The no-cloning theorem is a central topic in quantum cloning and information processing systems, influencing how quantum communication is understood.
"Quantum Cloning and Information Processing Systems"No-Cloning Theorem (2009)
[6] supported
The no-communication theorem asserts that it is impossible for one observer to transmit information to another during the measurement of an entangled quantum state, regardless of spatial separation.
"It asserts that during the measurement of an entangled quantum state , it is impossible for one observer to transmit information to another observer, regardless of their spatial separation."No-communication theorem
[7] supported
A necessary condition for the theorem to hold is that neither observer (Alice or Bob) is allowed to affect the preparation of the initial quantum state.
"An important assumption going into the theorem is that neither Alice nor Bob is allowed, in any way, to affect the preparation of the initial state."No-communication theorem
[8] supported
If an observer were allowed to participate in the preparation of the initial state, they could trivially encode a message into it, which would bypass the no-communication restriction.
"If Alice were allowed to take part in the preparation of the initial state, it would be trivially easy for her to encode a message into it; thus neither Alice nor Bob participates in the preparation of the initial state."No-communication theorem
[9] supported
The theorem states that given a prepared initial state, there is no action one observer can take on their portion of the system that would be detectable by the other observer.
"Simply, the theorem states that, given some initial state, prepared in some way, there is no action that Alice can take that would be detectable by Bob."No-communication theorem
[10] supported
The mathematical proof relies on showing that the partial trace of the system over the first observer's subspace remains unchanged as they perform measurements, meaning the second observer cannot distinguish pre- and post-measurement states.
"The goal of the theorem is to prove that Bob cannot in any way distinguish the pre-measurement state σ from the post-measurement state P (σ). This is accomplished mathematically by comparing the trace of σ and the trace of P (σ), with the trace being taken over the subspace H A ."No-communication theorem
[11] supported
The document does not discuss sealed messages or replies; it frames causal structure as describing which events can influence which others, and a closed timelike curve is the closed-loop case that would allow a signal to return to its own past.
"The causal relations between points in the manifold are interpreted as describing which events in spacetime can influence which other events."Causal structure
[12] supported
Sending a qubit into the past through a postselected closed timelike curve (P-CTC) is analogous to teleporting the qubit's state, which is how the paper frames the backward-in-time mechanism.
"Sending a qubit into the past by a P-CTC is somewhat like teleporting the qubit’s state"Perfect State Distinguishability and Computational Speedups with Postselected Closed Timelike Curves (2011)
[13] supported
A closed timelike curve is defined as a closed curve that is everywhere future-directed timelike (or everywhere past-directed timelike), which is the kind of loop a two-way causal exchange would require.
"A closed timelike curve is a closed curve which is everywhere future-directed timelike (or everywhere past-directed timelike)."Causal structure
[14] supported
In general relativity, a closed timelike curve is a hypothetical construct: a worldline that loops back on itself so a particle can return to and interact with its own past.
"describes a worldline in spacetime looping back on itself, allowing a particle to return to and interact with its own past"Experimental simulation of postselected closed timelike curves for decoding scrambled quantum information (2026)
[15] supported
Bennett and Schumacher's postselected quantum teleportation is the basis for a model of closed timelike curves that gives physically different results from Deutsch's model.
"Bennett and Schumacher’s postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch’s model."Perfect State Distinguishability and Computational Speedups with Postselected Closed Timelike Curves (2011)
[16] supported
A closed null curve is the lightlike analogue, defined as a closed curve that is everywhere future-directed null (or everywhere past-directed null).
"A closed null curve is a closed curve which is everywhere future-directed null (or everywhere past-directed null)."Causal structure
[17] supported
General relativity permits closed timelike curves, which is the starting point for treating a message sent backward in time as physically possible.
"existence of closed timelike curves (CTCs) [1–4]"Retrocausal Capacity of a Quantum Channel: Communicating through Noisy Closed Timelike Curves (2026)
[18] supported
Under the postselected model, the future existence of a P-CTC can affect the present outcome of an experiment, unlike in Deutsch's model.
"in which the future existence of a P-CTC might affect the present outcome of an experiment."Perfect State Distinguishability and Computational Speedups with Postselected Closed Timelike Curves (2011)
[19] supported
Combining forwards causality with retrocausality creates an ordering problem for dynamic production, because future events must produce past events while past events must also produce future events.
"because then the future events must produce the past events but also the past events must produce the future events"Two Roads to Retrocausality
[20] supported
Unconditionally secure bit commitment is forbidden by quantum mechanics.
"Unconditionallysecurebitcommitmentisforbiddenbyquantummechanics."Strong no-go theorem for Gaussian quantum bit commitment
[21] supported
The traditional picture of bit commitment is a one-way handover: Alice locks her bit in a safe, gives it to Bob, and later reveals it by handing over the key.
"Alice locks a secret bit into a safe that"Strong no-go theorem for Gaussian quantum bit commitment
[22] supported
Under immutable timeline retrocausality, a present event's backwards influence cannot change anything in the present because that influence has already been exerted.
"‘immutable timeline retrocausality,’ where an event in the present having a retrocausal influence on the past can’t change anything about the present because its retrocausal influence has already been exerted"Two Roads to Retrocausality
[23] supported
Price argued that the kind of retrocausality needed to explain Bell correlations cannot be used to create causal paradoxes such as a retrocausal grandfather paradox.
"Now as explored by Price in ref [15], it transpires that the kind of retrocausality needed to explain the Bell correlations actually can’t be used to create causal paradoxes of this kind"Two Roads to Retrocausality