Encoding and Decoding Quantum Information through Relativistic Quantum Fields in Curved Spacetimes

Keskeiset käsitteet

A relativistic quantum communication channel can be constructed between two localized qubit systems by coupling them to a relativistic quantum field in arbitrary curved spacetimes, allowing for the theoretical maximum quantum capacity.

Tiivistelmä

The authors construct a relativistic quantum communication channel between two localized qubit systems, mediated by a relativistic quantum field, that can achieve the theoretical maximum for the quantum capacity in arbitrary curved spacetimes using the Unruh-DeWitt (UDW) detector formalism.
Key highlights:

They use techniques from algebraic quantum field theory (AQFT) to express the quantum capacity of the quantum communication channel purely in terms of the correlation functions of the field and the causal propagator for the wave equation.
This ensures the resulting quantum channel and quantum capacity are manifestly covariant, respect the causal structure of spacetime, and are independent of the details of the background geometry, topology, and the choice of Hilbert space (quasifree) representations of the field.
The protocol involves Alice encoding her qubit state into the quantum field through a specific unitary operation, and Bob decoding the state from the field into his own qubit system.
The conditions for achieving a perfect quantum channel require the field correlation functions to satisfy certain constraints on the eigenvalues and strengths of the field interactions.
This extends previous results on relativistic quantum communication in flat spacetimes to arbitrary curved spacetimes.

Tilastot

E(f1, f2) = π/4 mod 2π
E(f1, f2)^2 >> W(f2, f2)

Lainaukset

"We construct a relativistic quantum communication channel between two localized qubit systems, mediated by a relativistic quantum field, that can achieve the theoretical maximum for the quantum capacity in arbitrary curved spacetimes using the Unruh-DeWitt detector formalism."
"Crucially, what we gain from this will not be a simple rewriting of all the formulae in the literature: we will see that the quality of the relativistic quantum channel mediated by the quantum scalar field can be formulated purely in terms of smeared correlation functions of the field and the detector parameters."

Tärkeimmät oivallukset

Transmission of quantum information through quantum fields in curved spacetimes

by Michael Kasp... klo arxiv.org 10-02-2024

https://arxiv.org/pdf/2408.00518.pdf

Syvällisempiä Kysymyksiä

How would the protocol need to be modified if the field is not a scalar field but a vector field like the electromagnetic field?

If the quantum communication protocol is adapted to utilize a vector field, such as the electromagnetic field, several modifications would be necessary. First, the Unruh-DeWitt (UDW) detector model, which is designed for scalar fields, would need to account for the additional degrees of freedom associated with vector fields. This involves considering the polarization states of the electromagnetic field, which introduces complexities in the coupling between the qubit detectors and the field.
In the case of a vector field, the interaction Hamiltonian would need to be modified to include terms that couple to the vector potential ( \hat{A} ) of the electromagnetic field. The interaction could take the form:
[
\hat{h}_I = \sum_i \lambda_i \hat{m}_i(\tau) \cdot \hat{A}(x),
]
where ( \hat{m}_i(\tau) ) represents the qubit operators and ( \hat{A}(x) ) is the vector potential. The coupling would need to respect the gauge invariance of the electromagnetic field, which may impose additional constraints on the choice of smearing functions and the interaction profile.
Moreover, the coherent states used in the protocol would need to be generalized to account for the polarization of the vector field. This means that Alice and Bob would need to encode and decode their qubit states not only in terms of the amplitude of the field but also its polarization states. The protocol would thus involve a more complex analysis of the correlation functions and the causal propagators, as the vector field's degrees of freedom could lead to different entanglement structures and transmission capacities.

What are the implications of the existence of multiple unitarily inequivalent vacuum states in curved spacetimes on the performance of the quantum communication channel?

The existence of multiple unitarily inequivalent vacuum states in curved spacetimes has significant implications for the performance of the quantum communication channel. Each vacuum state corresponds to a different choice of the ground state of the quantum field, which can affect the correlation functions and the overall structure of the quantum channel.
In particular, the choice of vacuum state influences the Wightman functions, which are crucial for determining the quantum capacity of the channel. Different vacuum states can lead to variations in the entanglement structure of the field, which in turn affects the ability of Alice and Bob to transmit quantum information. For instance, if Alice and Bob are using a vacuum state that is not the same, the correlations they rely on for communication may be diminished, leading to a lower quantum capacity.
Furthermore, the presence of unitarily inequivalent vacuum states can introduce challenges in ensuring that the communication protocol is robust against changes in the background geometry. If the vacuum state is not well-defined or if Alice and Bob are in different frames of reference, the effectiveness of the quantum channel may be compromised. This necessitates careful consideration of the vacuum state in the design of the communication protocol, potentially requiring adaptive strategies to optimize the transmission of quantum information.

Can this framework be extended to study the transmission of entanglement or other quantum resources between distant parties through the quantum field?

Yes, the framework established for the transmission of quantum information can indeed be extended to study the transmission of entanglement and other quantum resources between distant parties through the quantum field. The underlying principles of the protocol, which involve encoding and decoding qubit states via the interaction with a quantum field, can be adapted to focus on entangled states.
To study entanglement transmission, one could consider scenarios where Alice prepares an entangled state shared with a third party (e.g., a quantum state that is entangled with Bob's system). The protocol would then involve Alice encoding her part of the entangled state into the quantum field, while Bob decodes it, effectively transferring the entanglement through the field. The performance of this entanglement transmission would depend on the same factors that influence the quantum capacity, such as the correlation functions and the causal structure of the spacetime.
Moreover, the framework could be generalized to explore the transmission of other quantum resources, such as quantum coherence or quantum discord, by modifying the encoding and decoding operations to account for the specific properties of these resources. This would involve analyzing how these resources interact with the quantum field and how they can be preserved or enhanced during transmission.
In summary, the established protocol for quantum communication can be effectively adapted to study the transmission of entanglement and other quantum resources, providing a rich avenue for exploring the interplay between quantum information theory and relativistic quantum field theory in curved spacetimes.