Retrocausal Teleportation Protocol
Time travel has long captured the human imagination, relegated to the realm of science fiction and fantasy. However, recent developments in quantum physics suggest that, at least at the quantum level, retrocausal effects—where future events influence the past—may be not only possible but experimentally testable. The retrocausal teleportation protocol, proposed by researchers from institutions including Hitachi Cambridge Laboratory, University of Cambridge, and the University of Maryland, represents a groundbreaking approach to exploring these temporal paradoxes through the lens of quantum mechanics.
While classical physics presents a deterministic universe where cause must precede effect, quantum mechanics and relativity theory paint a more nuanced picture. There are already well-known examples from relativity theory like wormholes, which are valid solutions of Einstein's Field Equations, and similarly in quantum mechanics the non-classical state of quantum entanglement—the "spooky action at a distance" that troubled Einstein—which demonstrates that quantum systems can maintain instantaneous correlations across space and, potentially, time.
Perhaps most intriguingly, the protocol suggests that quantum entanglement can be used to effectively send information about optimal measurement settings "back in time"—information that would normally only be available after an experiment is complete. This capability, while probabilistic in nature, could revolutionize quantum computing and measurement techniques. Recent advances in multipartite hybrid entanglement even suggest these effects might be achievable in real-world conditions, despite environmental noise and interference.
This article explores the theoretical foundations, experimental proposals, and potential applications of the retrocausal teleportation protocol. From its origins in quantum mechanics and relativity theory to its implications for our understanding of causality and the nature of time itself, we examine how this cutting-edge research challenges our classical intuitions while opening new possibilities for quantum technology. As we delve into these concepts, we'll see how the seemingly fantastic notion of time travel finds a subtle but profound expression in the quantum realm, potentially revolutionizing our approach to quantum computation and measurement while deepening our understanding of the universe's temporal fabric.
Introduction
Classical Newtonian physics painted a picture of the world that was predictable, deterministic, and some might even say common sensical. Physical systems and particle-to-particle interactions can be explained by force, mass (F = ma) and Newton's laws of motion. Also, a seemingly common sense notion from classical mechanics is that there are very definite cause-and-effect relationships, with things that happen in the past determining present conditions and never the other way around. In classical physics this would make it possible, at least theoretically, to completely describe the past state and future trajectory of a system with absolute precision by extrapolating from its present configuration. However, with relativity and quantum mechanics, what are called non-classical physics, the behavior of nature becomes a little more—let’s say— “non-linear”, and even within the standard model some classical notions associated with Newtonian mechanics become obsolete.
One such situation is what are called closed time-like curves (CTCs), which are essentially “loops” in spacetime that can naturally emerge from Einstein field equations (EFE) under certain circumstances—for instance CTCs are naturally emergent in Gödel solution of EFE—and describe a trajectory (called a world line in relativity) that returns to the same point in space and time, effectively describing a spacetime geometry permitting time travel, or at the very least losing the causal distinction of “before” and “after” because, as Einstein described it: “…the distinction ‘earlier-later’ is abandoned for world-points which lie far apart in a cosmological sense, and those paradoxes, regarding the direction of the causal connection, arise, of which Mr. Gödel has spoken” [1].
So, we see that closed time-like curves arise with relative ease in relativity and are predicted in natural systems, for example within the ergosphere of black holes. These causally ambiguous loops also arise within quantum physics because the quantum vacuum is an entangled state, with both non-classical correlations in space-like and time-like regions. That means non-local connections between causally separated regions in space and time, i.e., closed time-like curves. This gives rise to effects like Unruh thermalization and emission of photons from the vacuum—recently observed and measured—which occurs because the vacuum state of the electromagnetic field has intrinsic quantum entanglement between past and future states [2, 3, 4]. This raises the question, can entanglement be used to influence “past” events?
The fact that CTCs are found in both relativity and quantum mechanics has a potentially straight-forward answer, which can speak to the physical relevance of closed-timelike loops in spacetime. The solution comes when it is realized that quantum entanglement—sometimes referred to as Bell pairs or Einstein-Podolsky-Rosen correlations (EPR)—is multiply connected spacetime geometry, also known as Einstein-Rosen bridges (ER) such that ER = EPR [5] (a resolution to the EPR paradox first proposed by Einstein, Podolsky, and Rosen). So, both relativity and QM say that time travel is possible, with some observable effects being the result of non-local connections or spacetime entanglement “loops”, and aspects as fundamental as time symmetry seeming to require retrocausality [6, 7].
Interesting results begin to emerge when considering quantum field theory in curved spacetimes (QFT in CST)—we will just focus on some specifics here and not the more general ramifications of a Unified Field Theory— because we can analyze the behavior of quantum systems, like qubits, in the presence of closed time-like curves, for example modeling the nonlinearities that arise from a qubit interacting with an older version of itself in a CTC [8]. The study of these systems provides valuable insight into nonlinearities and the emergence of causal structures in quantum mechanics—essential for any formulation of a quantum theory of gravity.
Significantly, they have implications for quantum theories of time travel. In quantum physics there is an experimental program generally referred to as quantum teleportation (QT) that enables the transfer of quantum information states via a classical channel by leveraging the strong correlation between quantum entangled systems (QT protocols have also been utilized to transfer energy and may soon verify the ER = EPR conjecture). Standard quantum teleportation relies on quantum entanglement and classical communication to transfer the state of a particle from one location to another without directly transferring the particle itself (the classical communication channel ensures that signals are not transferred instantaneously or faster than light).
Understanding Quantum Teleportation
Before we explore the proposed experiment to send a quantum state “back” in time, a general understanding of the QT protocol must be established. Quantum teleportation transfers a quantum state between two parties (Alice and Bob) using entanglement and classical communication (Figure 1). The key steps are:
Entanglement Creation:
Alice and Bob share an entangled pair of qubits.
State to Teleport:
Alice has an additional qubit with the quantum state ∣ψ⟩| she wants to teleport.
Bell-State Measurement:
Alice performs a Bell-state measurement on her qubit (to be teleported) and her half of the entangled pair, collapsing the system into one of four possible entangled states.
Classical Communication:
Alice sends the measurement result (two classical bits) to Bob.
State Reconstruction:
Bob applies a corresponding quantum operation (e.g., X, Z gates) to his qubit based on Alice’s result, recreating ∣ψ⟩| perfectly.
Note: The original state ∣ψ⟩| is destroyed during the process, preserving the no-cloning theorem.
Figure 1. Illustration of the QT protocol. The protocol consists of four steps. In the first step, the entangled qubit is shared between Alice and Bob. With local operations, Alice entangles the target qubit with the entangled pair (step 2). Then, Alice measures both of her qubits (step 3) and tells Bob the result of the measurement via classical communication. He can then correct his qubit (step 4) and Alice’s state is teleported to Bob (Step 5). Image and image description from Fitzgerald 2024 https://www.researchgate.net/publication/379970865_A_Christmas_story_about_quantum_teleportation
The State of the Art
Advancements in QT protocols have significantly benefited from developments in entanglement swapping and the efficiency of Bell state measurements (BSMs), the latter being named after the famous Bell inequality formulations that define the non-classical nature of certain measurement outcomes with quantum systems, like photonic qubits (entangled photons used to create quantum bits). These innovations are pivotal for enhancing the reliability and scalability of quantum communication networks, which gives direct technological applicability of QT techniques. For instance, entanglement swapping enhancements have including extended entanglement distribution, in which entanglement swapping enables the entanglement of two particles that have never interacted directly, facilitating the extension of entangled links across distant nodes in a quantum network (this technique is similar to entanglement harvesting protocols, which we have recently discussed in recent articles). This principle is fundamental for the development of quantum repeaters, which are essential for long-distance quantum communication. As well improvements in BSMs have been realized with techniques such as boosted quantum teleportation [9].
Combining entanglement swapping with improved BSM efficiency is crucial for the development of quantum repeaters. These devices facilitate the distribution of entanglement over long distances by segmenting the communication channel into shorter links and swapping entanglement between them [10]. As well, these advancements should facilitate the design of hybrid quantum networks, since advances in entanglement swapping protocols have enabled the interconnection of heterogeneous quantum systems, such as linking discrete-variable and continuous-variable nodes, essentially utilizing both the particle (discrete) and wave (continuous) nature of light [11]. This capability is vital for the realization of versatile and robust quantum networks.
QT is not only a key enabler for the development of quantum computing systems and networks but also a cornerstone for secure, tamper-proof communication protocols. These applications hold promises for advancing technology in areas such as cryptography, distributed computing, and global connectivity. Recent studies have shown that these possibilities are nearing experimental realization, the second step in full implementation of quantum non-locality in technology.
For those with an eye to the future, there is an exciting new class of teleportation protocols that may enable remarkable experimental tests of quantum theory, for example to test retrocausality in quantum mechanics—the ability to perform operations to change the past state of a quantum system, like a qubit—for example by performing post-selected teleportation (P-CTCs) [12]. If entanglement is a kind of spatial nonlocality, retrocausal action is a kind of temporal nonlocality, and should be just as realizable as entanglement of spatially separated quanta. This would mean that just as entanglement is utilized in quantum teleportation protocols for quantum networks and computing, these may be vastly advanced with retrocausal entanglement protocols that can improve quantum robustness by leaps and bounds. As well as revealing fundamental properties of our reality, like retrocausal or trans-temporal interactions (nonlocality in space and time), in which future or present states can affect—or be the cause of in a retroactive way—past states.
1.1 The Quantum Mechanics of Time Travel
Researchers have found that the quantum mechanics of closed timelike curves does allow for quantum time travel, which differs from the classical conception of time travel in a few ways, most namely of which is that proposed protocols do not enable paradoxical causal violations and primarily have implications for enhancing quantum measurements—what is called quantum metrology, which are techniques that can leverage certain effects to overcome limits on conventional observation and measurement—and potentially boosting the power of computation.
The interesting thing about microscopic or quantum phenomena is that they can have retrocausal mechanics without violating relativity theory or the strong principle of causality: that a cause must always precede its effects. In relativity, the strong principle can be restated as ‘no information can be sent faster than the speed of light’, which can be called the weak principle of causality. A clear example of how quantum mechanics can be retrocausal without apparent violation of the strong or weak principles of causality is given in David Pegg’s review Retrocausality and Quantum Measurement [13]. Classical electromagnetism (EM) involves quadratic equations that when solved give two answers, which essentially amount to a solution in which an oscillating charge (an emitter) generates EM radiation that goes “forward in time” (what for historical reasons was called “retarded potentials”) and simultaneously an absorber that has sent advanced radiation before the emitter has sent the forward potentials and the energy that is dissipated by the emitter is due to the radiative reaction force of the absorber, such that preceding event (emitted radiation and loss of energy by the charged oscillator) is caused by the future event (absorption of radiation).
Since the advanced radiation involves advanced potentials that act retrocausally on the emitter, this is omitted in the classical interpretation because it would seem to violate the strong principle of causality. However, two brilliant physicists John Wheeler and Richard Feynman re-evaluated the theory of EM and constructed a formulation that retains both the retarded and advanced potentials: what is called Wheeler-Feynman absorber theory of radiation. This theory forms the basis of Cramer’s Transactional Interpretation of quantum mechanics, and although absorber theory contravenes the strong principle of causality, in a universe with perfect absorbing properties it does not violate the weak principle (no macroscopic messages can be sent back in time between two observers) and it predicts precisely the same experimentally verifiable results as the conventional, temporally-unidirectional theory of electrodynamics.
There are other examples in which a retrocausal explanation seems to be more precise to the actual mechanics involved, such as the retrodiction problem in quantum mechanics— Quantum retrodiction involves finding the probabilities for various preparation events given a measurement event—in which backward time evolution of a BSM on an unknown quantum state to influence the preparation of the state before it is sent is shown to be the easiest explanation [14].
The quantum picture that is retrocausal in the sense of violating the strong but not the weak principle of causality can be extended beyond the use of a state evolving backwards in time for retrodictive purposes… we use a retrocausal quantum picture to examine the possibility of preparing a qubit state evolving forwards in time in the normal manner, then sending this state into the past where it appears as an identical forward evolving qubit state that can be measured in the normal manner or used for other purposes. We see that this can only be done on a probabilistic basis that does not violate weak causality, but it is still useful for the main application… that of measuring a quantum optical qubit state before it is prepared.
In the example given by Pegg, CTCs in quantum mechanics could enable instantaneous quantum communication without violating the weak principle of causality (no FTL signaling). While the existence of closed timelike curves is hypothetical, they can be simulated probabilistically by QT circuits.
Can quantum mechanics allow us to effectively send information back in time? Research is needed to answer this question, and progress has recently been made with a new study by researchers from Hitachi Cambridge Laboratory, University of Cambridge, Paul Scherrer Institute, ETH Zürich, and the University of Maryland. The researchers have devised an experiment to test the question of quantum non-locality in time with a novel twist on the long-standing hypothetical method of P-CTCs, quantum retrodiction, and instantaneous quantum computation. In their paper "Nonclassical Advantage in Metrology Established via Quantum Simulations of Hypothetical Closed Timelike Curves," the researchers describe a thought experiment where quantum entanglement is used to simulate sending information backwards in time through a CTC [15], via the basic procedures of QT, but with the inclusion of a particle in a specially prepared quantum state that is sent "back in time" via interaction of entangled EPR pairs (a kind of entangled quantum circuit) to change a particle's state in the past; a retrocausal mechanism. While actual time travel remains in the realm of science fiction, the researchers show how quantum circuits can probabilistically simulate CTCs in a way that provides a practical advantage for quantum measurements. The protocol is outlined as follows (Figure 2):
Figure 2. Schematic outline of the steps involved in sending a quantum state “back” in time for a post-selected teleportation measurement or P-CTC. Image from Quantum time travel: The experiment to 'send a particle into the past', By Miriam Frankel, for NewScientist, May 2024.
It can be seen that the basic premise follows elements of the conventional teleportation protocol, however instead of transferring the quantum state of particle A to particle D, particle D is prepared in the ideal state that the experimenter wants particle A to be in, which upon interaction of particle A’s entangled particle pair, B, there is a small probability that the Bell state measurement will propagate “backwards” in time to project onto particle A, thus retrocausally changing particle A’s quantum state to the desired spin. Since this can’t be utilized to send messages back in time, it does not violate the weak principle of causality, and hence is fully compatible with relativity, which in any case has solutions that are CTCs. Do CTCs like the ‘loop the loop’ of retrocausal teleportation offer empirical verification of the CTCs in relativity? So that they should not be discarded like the advanced potentials in quantum electrodynamics (viz-a-viz Wheeler-Feynman absorber theory).
The key insight is that quantum entanglement manipulation can effectively allow a quantum metrologist to "send back in time" information about the optimal measurement settings - information that would normally only be available after an experiment is complete. While this simulated time travel sometimes fails, when it succeeds it enables measurements that extract more information per probe than would be classically possible.
This work demonstrates a fascinating connection between quantum entanglement and apparent retrocausal effects that can generate real operational advantages forbidden by classical physics. While falling short of actual time travel, it shows how the strange properties of quantum mechanics might be harnessed in unexpected ways that challenge our usual notions of causality while potentially enabling practical improvements in quantum sensing and measurement.
Perhaps most significantly, understanding the full mechanics of what is occurring during retrocausal protocols gives insight into quantum theory itself. Since the P-CTC protocols do not violate the weak principle of causality they cannot be used for faster-than-light communication, and in that way the results remain the same as in orthodox quantum formalisms; the only difference is the interpretation of what is occurring. Positing a retrocausal mechanism removes the need for “state reduction” or a collapse of the wavefunction (describing a superposition). This offers some conceptual advantages, and perhaps greater compatibility with relativity (e.g., CTCs and ER = EPR) for a fully cogent theory of unified physics.
“Our Gedankenexperiment demonstrates that entanglement can generate operational advantages forbidden in classical chronology-respecting theories.” - Arvidsson-Shukur et al., 2024 [15].
The experiment is yet to be performed, and the latest data only comes from testing the scenario in a simulation, however this provides evidence of the feasibility of the proposed protocol, which is out of the norm to say the least; imagine telling friends and colleagues that you are working on an experiment to teleport particles back in time.
Probabilistic Instantaneous Quantum Computation
The retrocausal teleportation protocol stems from the related notion of retrodiction in quantum mechanics, which as we saw is most easily explained via a retrocausal mechanism. A highly interesting corollary that also emerges from this line of investigation—and which has significant implications for quantum computation technology—is that the principle of teleportation can be used to perform a quantum computation even before its quantum input is defined [16]. This effectively would enable instantaneous quantum computation by utilizing the entanglement state of qubits whose past state is amenable via future BSMs (Bell state measurements).
This procedure essentially implements the QT and P-CTC methodologies to receive, in a probabilistic manner, some outputs of a quantum computation instantaneously, such that if a quantum computation would normally take an arbitrarily long time, a P-CTC protocol can be utilized to obtain the exact output state instantaneously. The hypothetical procedure is outlined as follows (Figure 3):
Figure 3. a) Conventional scheme: At time t1 the engineer is given the input qubits 1 of the quantum computation (QC) in a quantum state unknown to her. She feeds them into her quantum computer and starts the computation. The computation is very time-consuming, so that the quantum computer does not terminate before the deadline at t2. b) Scheme for instantaneous quantum computation: At a time earlier than t1 the engineer has fed qubits 3, which are each maximally entangled with one qubit 2, into her quantum computer and has done the computation. At the later time t1 when the input qubits 1 are given to her the engineer performs a Bellstate measurement (BSM) on each pair of qubits 1 and 2 and projects qubits 3 onto a corresponding state. In a certain exponentially small fraction of cases the computational time is saved completely as she immediately knows that qubits 3 are projected onto the output state resulting from the correct input one. Image and image description from- Č. Brukner, J.-W. Pan, C. Simon, G. Weihs, and A. Zeilinger, “Probabilistic instantaneous quantum computation,” Phys. Rev. A, vol. 67, no. 3, p. 034304, Mar. 2003, doi:10.1103/PhysRevA.67.034304 [16].
Can quantum time travel be utilized beyond improving quantum computers, like sending people “back” in time? Some of the originators of the concept of P-CTC like Seth Lloyd caution against such notions because the retrocausal teleportation protocols currently require strong quantum entanglement, which requires stringently controlled isolation and hence there is no way that all the particles of an entire human body are going to be prepared in a strong entanglement state and enable trans-temporal activity. However, recent advancements in teleportation techniques have found that QT can be achieved in the presence of environmental interactions (noise) by utilizing multipartite hybrid entanglement of many-body systems [17]. So, don’t discount the possibility out-of-hand, because there are indications that the weak and strong principles of causality can in special circumstances be bypassed and the multiply connected entanglement network of spacetime [18] is accessible even to large quantum systems like humans.
Highlights
The retrocausal teleportation protocol represents one of the most fascinating frontiers in quantum physics, where the classical notion of cause and effect meets the bizarre quantum realm. Through careful manipulation of quantum entanglement, researchers have theoretically demonstrated that it may be possible to influence quantum states in the past, without violating the fundamental principles of relativity or causality that govern our universe.
The protocol builds upon conventional quantum teleportation techniques, which already enable the transfer of quantum states between locations using entanglement and classical communication. However, this new approach takes quantum teleportation into uncharted territory by leveraging closed timelike curves (CTCs) - theoretical constructs that emerge naturally from Einstein's field equations and quantum mechanics. While actual time travel remains firmly in the realm of science fiction, these quantum simulations of CTCs could enable practical advantages in quantum metrology and computation.
Perhaps most remarkably, the retrocausal protocol suggests that quantum entanglement can be used to effectively send information about optimal measurement settings "back in time" - information that would normally only be available after an experiment is complete. While this process is probabilistic and cannot be used for faster-than-light communication or sending macroscopic objects through time, it demonstrates how quantum mechanics continues to challenge our conventional understanding of causality and time's arrow.
The implications extend far beyond pure theoretical physics. The ability to perform quantum computations before their inputs are even defined, as demonstrated in probabilistic instantaneous quantum computation, could revolutionize quantum computing technology. Moreover, recent advances in multipartite hybrid entanglement suggest that these effects might be achievable even in noisy, real-world conditions.
As we continue to probe the boundaries between quantum mechanics and relativity, the retrocausal teleportation protocol serves as a powerful reminder that our universe is far stranger and more interconnected than classical physics would suggest. The multiply connected nature of spacetime through quantum entanglement - elegantly captured in the ER=EPR correspondence - hints at a deeper reality where past, present, and future may be more intimately linked than we ever imagined.
While the time travel of science fiction may remain far too advanced for our current understanding of spacetime, these quantum protocols are opening new windows into the nature of time itself, suggesting that causality at the quantum level is far more subtle and fascinating than our everyday experience would suggest. As we continue to develop and refine these techniques, they may not only advance our technological capabilities but also fundamentally reshape our understanding of reality's temporal fabric.
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