Relativistic Quantum Information

• Relativistic Quantum Information is a field that extends quantum information theory to incorporate relativistic effects, leading to observer-dependent entanglement and altered communication capacities.
• The discipline uses quantum field theory, detector models, and path-integral methods to assess entropic measures, fermionic algebra, and quantum channel dynamics in curved and accelerated spacetimes.
• Insights from RQI are crucial for designing quantum protocols near black holes and high-acceleration environments, impacting quantum communication and computation in relativistic settings.

Relativistic Quantum Information (RQI) is the field dedicated to understanding how quantum informational quantities—especially entanglement, communication capacity, and observable statistics—behave when subject to the constraints and effects of relativity. This encompasses both special and general relativistic scenarios, including non-inertial motion (e.g., accelerated detectors), quantum fields in curved spacetime (e.g., near black holes), and the implementation of quantum information protocols in environments where relativistic considerations are unavoidable. The framework builds on quantum information theory, quantum field theory, and general relativity, revealing fundamentally new phenomena such as observer-dependent entanglement and the observer-relativity of quantum communication resources.

1. Conceptual Foundations and Scope

RQI generalizes quantum information theory (QIT) to contexts where relativistic effects dominate the dynamics or observability of quantum systems. This involves situations where:

• Quantum systems propagate or interact in spacetime regions with significant curvature or acceleration.
• The quantum fields mediating interactions may themselves be affected by gravitational or inertial effects.
• Information carriers—matter, photons, or quasi-particles—undergo Lorentz transformations, resulting in alterations of entropic quantities, decoherence rates, and entanglement structure.

Key motivations include understanding quantum communication near black holes, studying information-theoretic signatures of spacetime geometry, and probing the quantum–classical boundary in relativistic quantum fields (Martin-Martinez, 2011).

The scope of RQI extends to both theoretical milestones—such as combining von Neumann entropy with general relativistic concepts (Adami, 2011)—and practical proposals for extracting quantum information resources in real-world relativistic environments.

2. Observer Dependence and Frame-Relativity

A foundational insight of RQI is that entanglement, purity, and related quantum correlations are not invariant across reference frames. For inertial observers, Lorentz transformations mix internal (spin, polarization) and external (momentum) degrees of freedom, leading to observer-dependent reduced states and entropies.

For instance, the reduced density matrix of a spin-1/2 particle, or a bipartite Bell state, changes under Lorentz boosts. This is because particle spin (or polarization) becomes entangled with momentum under such transformations, and when the momentum is traced out (as in measurement statistics), the spin subsystem generally evolves from pure to mixed (Ralph et al., 2011, Adami, 2011).

For non-inertial (accelerated) observers, phenomena such as the Unruh effect appear: the Minkowski vacuum is perceived as a thermal state, resulting in thermal decoherence and, in many regimes, the sudden death or significant degradation of entanglement (Ralph et al., 2011). The transition rate of realistic detectors, such as spatially-extended Unruh–DeWitt models, depends explicitly on proper acceleration, spatial profile, and coupling to the field (Lee, 2013).

The observer-relativity of quantum information is thus operationalized by the transformation laws for states and observables and is manifest experimentally in relativistic corrections to quantum communication and computation protocols.

3. Algebraic Structure, Superselection Rules, and Entanglement

The evaluation of entropic and entanglement-related quantities in RQI must account for the algebraic properties of quantum fields, especially for fermions. The canonical anticommutation relations (CAR) dictate a braided (or twisted) tensor product structure for fermionic modes:

$$a^\dagger b^\dagger |{\rm vac}\rangle \neq b^\dagger a^\dagger |{\rm vac}\rangle,$$

and

$\{a, a^\dagger\} = 1, \qquad \{a, b\} = 0.$

A fundamental superselection rule—parity—arises from Lorentz invariance via the spin-statistics theorem. States with even and odd fermion number cannot be coherently superposed; the allowed state space is confined to either even or odd parity sectors (Friis, 2015). Ignoring these structures can lead to ill-defined entanglement measures: for instance, the reduced density matrices for a bipartition of the fermionic Fock space do not, in general, share the same spectra unless parity is imposed (Bradler, 2011, Friis, 2015). Consequently, entanglement quantification for fermionic systems must enforce these algebraic and superselection constraints to be meaningful.

Similar phenomena arise for anyonic systems: RQI measures such as entanglement entropy and negativity interpolate between bosonic and fermionic behaviors as a function of the statistical parameter $\alpha$—semions at $\alpha=0.5$ exhibit minimum quantum Fisher information, demonstrating distinctly intermediate quantum-information-theoretic characteristics (Esmaeilifar et al., 2018).

4. Quantum Channels, Operational Capacities, and Causality

An essential lesson from RQI is that entanglement alone is not a reliable indicator of operational capability for quantum information tasks. The quantum channel capacity—formally rooted in quantum Shannon theory—directly quantifies the rate (possibly zero) at which quantum information can be transmitted through a relativistic process, regardless of whether some form of entanglement survives (Bradler, 2011).

In non-inertial frames or curved spacetime, it is possible for entanglement to remain nonzero while channel capacity vanishes, indicating that no quantum communication is possible. For example, in the infinite acceleration limit of the Unruh effect for fermionic channels, entanglement entropy may be nonzero while the channel's quantum capacity drops to zero.

RQI demands the careful modeling of communication protocols using quantum channels, described by completely positive trace-preserving maps. The explicit Kraus representations, channel capacities, and related operational metrics are determined by the relativistic dynamics of the field–detector system, detector switching functions, and the presence of boundaries or horizons.

Relativistic causality is safeguarded by the algebraic structure of quantum field theory (QFT) and, in practical calculation, by the strict vanishing of causal propagators for spacelike-separated regions (Tjoa, 2022). Models using algebraic QFT combined with detector-based approaches (such as Unruh–DeWitt detectors with covariantly defined smearing functions) allow for operational, nonperturbative analyses of scenarios historically considered paradoxical, as in the Fermi two-atom problem (Tjoa, 2022). Here, causality is maintained even when entanglement and measurement processes are considered in curved spacetime or in regimes where direct inspection of field modes, rather than local observables, is nontrivial.

5. Resource Harvesting, Field-Mediated Gates, and Experimental Realizations

RQI provides a framework for understanding extraction and manipulation of nonclassical resources from fields in a spacetime context. Key concepts include:

• Entanglement harvesting: Localized detectors (qubits or qutrits) locally interacting with fields can become entangled even when spacelike separated, extracting vacuum correlations (Lee, 2013, Perche et al., 2022).
• Magic resource harvesting: The extraction of non-stabilizerness (magic), essential for universal quantum computation, can be achieved via qutrit Unruh–DeWitt detectors. Analytic expressions in anti-de Sitter spacetime show that stronger curvature and higher dimensionality reduce the extractable non-stabilizer resource, as seen from the derived mana discriminant $\Delta=-(q+2\beta)$ as a function of transition probability $q$ and coherence $\beta$ (Yang et al., 22 Aug 2025).
• Universal field-mediated quantum gates: The Unruh–DeWitt detector formalism enables the explicit construction of quantum gates (CNOT, SWAP, state transfer), with the field acting as a mediating channel. The performance of such gates is assessed by operational tools such as the diamond norm (Aspling et al., 15 Feb 2024, Aspling, 18 Jul 2024). Quantum Shannon theory metrics—mutual information, coherent information, channel capacity—quantify channel performance in relativistic and field-theoretic environments.

Platforms such as Tomonaga–Luttinger liquids and quantum materials with engineered edge states enable direct simulation and realization of RQI channels, with careful design constraints to maximize channel capacity and control decoherence via field–detector engineering (Aspling, 18 Jul 2024).

6. Relativistic State Updates, Covariance, and Conservation Laws

The definition and update of quantum states in a relativistic context is nontrivial, especially after selective (local) measurements. Standard quantum measurement protocols—instantaneous or global “collapses”—fail to respect causality or conservation laws in relativistic spacetimes.

The polyperspective formalism addresses this by promoting the quantum state to a multiplet $(\rho_A, \rho_B, \rho_{AB})$ defined on an extended Hilbert space $H_A \oplus H_B \oplus (H_A \otimes H_B)$ (Polo-Gómez et al., 23 Jun 2025). State updates are then context-sensitive: the local state $\rho_A$ is updated using only information in the causal past of $A$, and joint correlations $\rho_{AB}$ are updated using information in the union of causal pasts $A$ and $B$. This approach guarantees covariant, causally consistent state updates and preserves the correct joint measurement statistics and conservation laws—even across arbitrary spacelike hypersurfaces.

The polyperspective or “polystate” formalism may be essential for a rigorous treatment of relativistic measurement, distributed quantum information processing, and relativistic quantum cryptography.

7. Methodological Tools, Mathematical Structures, and Future Prospects

RQI employs advanced mathematical frameworks:

• Bundle and representation theory: The covariant description of localized qubits and spin relies on vector bundles over mass shells, with physically meaningful discrete degrees of freedom encoded as sections of these bundles. The Pauli–Lubansky four-vector replaces ambiguous (frame-dependent) Newton–Wigner spin as the proper invariant characterizing spin in relativistic settings (Lee, 2021, Lee, 2022).
• Quantum temporal probabilities (QTP) and closed-time-path (CTP) formalism: Measurement theory is extended to multi-time (unequal-time) events, calculated from path-integral and generating functional techniques tied to real-time evolution and non-equilibrium field theory (Anastopoulos et al., 2023).
• Path-integral derivations and renormalization group connections: Localized probe–field models are connected with particle detector descriptions (Unruh–DeWitt, harmonic oscillator probes) via Schwinger–Keldysh integrals, with systematic inclusion of corrections and explicit connection to Wilsonian effective field theory (Torres, 2023).

Future directions in RQI include resolving black hole information paradoxes, operationalizing quantum information protocols in deep-space environments, establishing complete covariant multi-party state descriptions, and determining the quantum character of putative gravitational fields through resource harvesting and quantum communication tests.

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Summary Table: Central Themes and Methods in Relativistic Quantum Information

Key Concept	Mathematical Structure	Operational/Physical Relevance
Observer dependence	Lorentz and Poincaré transformations	Entanglement, purity, and correlations are frame relative
Fermion/boson/anyon rules	CAR algebra, parity SSR, density matrices	Correct entanglement and resource quantification
Channel capacity	Kraus ops, channel maps, Shannon theory	Reliable quantum communication indicators
Detector models	UDW, harmonic oscillator, spatial profiles	Entanglement harvesting, quantum logic gates
State update/covariance	Polyperspective formalism, causal maps	Causally consistent measurement and conservation laws
Analytic/field-theory tools	CTP, QTP, path-integrals, bundle theory	Multi-time measurement, magic harvesting, effective models

The development of RQI continues to reveal new relationships between quantum information, spacetime geometry, quantum field theory, and the operational structures required for information-theoretic tasks in relativistic and gravitational environments.