Quantum superposition of black hole states as a communication resource

The gist: Quantum coherence in black hole spacetime degrees of freedom can allay the degradation of entanglement brought about by a black hole, thereby improving quantum communication protocols near the black hole.

Quantum Communication Near Classical Black Holes

The paper reviews quantum communication near a classical black hole, noting that treating the black hole classically leads to a fundamental decoherence of quantum systems and a degradation of quantum communication protocols that take place near the black hole’s event horizon Here, Alice and Rob both have access to a scalar fermionic (Grassmann) quantum field near the event horizon of a Schwarzschild black hole The initial maximally entangled state shared by Alice and Rob is given by ψ⟩AR = 0kA ⟩ + A0kR ⟩ + R + 1kA ⟩ + A1RkR ⟩ / √2 This state is maximally entangled for observers in free fall When Alice is free-falling and Rob is stationary above the event horizon, their respective vacuums differ, leading to a transformation of the state This results in the state becoming ψ⟩AR = 1/2 (cos squared r 0 0 cos r 0 sin squared r 0 0 cos r 1) / √2 Measuring the entanglement of this state using the negativity measure N [ρ] is found to be N [ξ(ρψ)] = cos squared r/2 The inertial maximally entangled state has therefore become a non-maximally entangled mixed state for Rob standing next to the event horizon of a black hole

Using Quantum Gravity as a Resource

The paper explores how quantum coherence in spacetime degrees of freedom can be used as a resource to allay the degradation of entanglement in proximity of the black hole The first assumption considered is that a black hole can be in a superposition of masses m1 and m2, possibly entangled with an auxiliary control system A superposition of masses of black holes can also occur naturally due to black hole evaporation With the black hole in a superposition of two masses, it is natural to expect its gravitational field, and therefore the structure of spacetime, to also be in a quantum superposition Assuming that Alice is always in free fall, and Rob is always standing above the event horizon (his Figure 2), Alice and Rob’s state ψ⟩AR of (1) would undergo a superposition of two channels with squeezing factors r1 and r2 defined by (4) with m replaced by m1 and m2 respectively This entanglement becomes entangled with the black hole and control [31] where 0⟩m and 1⟩m respectively denote the two mass states of the black hole with masses m1 and m2, and ψ⟩ AR 0 AR:= ψ⟩AR ⊗ 09kR ⟩ −

Quantum Capacity of Communication Channel

The quantum capacity of any channel is lower bounded by the coherent information of the channel, which in turn is lower bounded by the coherent information of the output state resulting from the action of the channel on one half of the maximally entangled state The effective channel described by (7) (arising from the superposition of two fermionic Gaussian amplification channels with squeezing factors r1, r2, respectively) can be thought of as a communication channel between Alice and Rob The difference in the coherent information between the superposition case and the classical mixture case can be used to quantify the effect of a superposition of black hole masses on quantum communication The coherent information of a bipartite quantum state ρˆAB is given by I(A, B)ρ = S(B)ρ − S(AB)ρ Figure 4 provides a density plot of the difference in the coherent information between the output state of the effective channel (7), arising from a superposition of two channels, and the corresponding output state for a classical mixture of the two channels, for r1 and r2 between 0 and π/4 We find that this difference is always positive, showing that the superposition of channels increases the ability to communicate quantum information between the two relativistic agents

N Superposition States

We have thus seen that an entangled state near a black hole decoheres less if the black hole is in a superposition of two masses compared to being in a classical mixture of two masses We found that as N increases, the decoherence decreases further However, it asymptotically converges before hitting zero decoherence – see Figure III B – due to the fact that there is only a single shared environment The generalization of the derivation above to the N-state superposition is straightforward The result with two mass states in a superposition (Figure 3) demonstrated that the greatest advantage in the decoherence rate is achieved when the squeezing parameters are maximally spaced

Discussion

We have shown that the possibility of quantum superpositions of black hole states with different masses can enhance the transmission of quantum information between two parties near the black hole This enhancement comes from an overall reduction of the noise due to the coherent superposition of different noisy channels [34–39] It is worth stressing that, in principle, quantum coherence in spacetime degrees of freedom could serve as a resource for quantum communication also beyond the black hole scenario discussed in this paper In many scenarios the contribution of quantum gravity is outweighed by that of other interactions The black hole scenario, instead, provides a setting where quantum aspects of gravity are expected to play a crucial role Our result provides a Gedankenexperiment highlighting that the fundamental decoherence expected in a classical theory of gravity can be mitigated by quantum effects In this context, our result provides a Gedankenexperiment highlighting that the fundamental decoherence expected in a classical theory of gravity can be mitigated by quantum effects Our Gedankenexperiment could in principle be simulated with analog systems, in a similar way as it was done for the simulation quantum field theory in curved spacetime with Bose-Einstein condensates (BECs) [40, 41] Under certain conditions, it is known that the phonons of a Bose gas can be described as effective photons propagating in a curved spacetime, with the metric being a function of the density and velocity flows of the condensate [42] An analogue of the entanglement entropy of the radiation has also been measured, finding a perfect match to that expected for real Hawking radiation [41]

Quantum Superposition

We consider a superposition of Hawking channels that have different values of squeezing parameter r but the same phase ϕ Taking a superposition of channels with the same squeezing parameter r but opposite phases ϕ1 = ϕ2 + π, and assuming a similar protocol to that assumed for a superposition of squeezing parameters, the posterior states after measuring the control in a +⟩c, −⟩c basis are ρˆ+AR:= 1/ (1 + cos squared r) (cos squared r 0 0 cos r 0 0 0 0 cos r 0 0) / √2 The average entanglement is then NAv[ˆρ] = cos r/2 <ref:2213.

1. Quantum Gravity Resource for Communication Capacity: The AI system can utilize quantum coherence in spacetime degrees of freedom to allay the (previously considered fundamental) decoherence of quantum systems, thereby improving the performance of quantum communication protocols performed in the black hole’s proximity. This implies an AI capable of designing communication protocols that are robust against gravitational decoherence by leveraging a superposition of two channels with squeezing factors r1 and r2 defined by (4).

2. Enhanced Quantum Teleportation Fidelity: The system can achieve improved fidelity for quantum teleportation near a black hole because the quantum superposition of channels increases the ability to communicate quantum information between the two relativistic agents. This allows for more reliable state transfer, specifically when comparing the superposition case and the classical mixture case, where the superposition of channels increases the ability to communicate quantum information between the two relativistic agents.

3. Superposition-Based Noise Reduction: The AI can implement a method for reducing noise by exploiting a coherent superposition of different noisy channels [34–39]. This capability allows the system to achieve an overall reduction of the noise, which directly translates to better performance in quantum communication tasks near gravitational sources.

4. Superposition Scaling for Increased Robustness: The AI can scale this benefit by considering a "superposition of N > 2 states, as increasing N leads to a further decrease in decoherence, although it asymptotically converges. This suggests the system can be designed for enhanced robustness by utilizing a superposition of N independent and identical decohering quantum channels for large N."