[Paper Review] Quantum communication in a superposition of causal orders

Sina Salek, Daniel Ebler+1 more|arXiv (Cornell University)|Sep 18, 2018

Quantum Information and CryptographyComputer Science47 citations

TL;DR

The paper shows that placing two noisy dephasing channels in a quantum superposition of orders can enable heralded noiseless quantum communication and can surpass the channels' individual quantum capacities in certain parameter regimes.

ABSTRACT

Quantum mechanics allows for situations where the relative order between two processes is entangled with a quantum degree of freedom. Here we show that such entanglement can enhance the ability to transmit quantum information over noisy communication channels. We consider two completely dephasing channels, which in normal conditions are unable to transmit any quantum information. We show that, when the two channels are traversed in an indefinite order, a quantum bit sent through them has a 25% probability to reach the receiver without any error. For partially dephasing channels, a similar advantage takes place deterministically: the amount of quantum information that can travel through two channels in a superposition of orders can be larger than the amount of quantum information that can travel through each channel individually.

Motivation & Objective

• Motivate extending quantum Shannon theory to scenarios where the order of channels is a quantum degree of freedom.
• Investigate whether a superposition of causal orders can enhance quantum information transmission through noisy channels.
• Demonstrate heralded noiseless transmission for completely dephasing channels and identify parameter regimes with deterministic capacity advantages.

Proposed method

• Model two quantum channels E and F acting on a state ρ with Kraus representations {Ei} and {Fj}.
• Apply the quantum SWITCH to obtain a higher-order channel Sω(E,F) whose Kraus operators encode the two possible orders EiFj and FjEi conditioned on an order qubit state ω.
• Compute the output state for ω = |+><+| and analyze diagonal and off-diagonal terms to show heralded noiseless transmission when measuring the order qubit.
• Evaluate the coherent information Q(·) of the switched channel to compare its quantum capacity with those of E and F.
• Use degradable-channel capacities Q(E)=1−H2(p) and Q(F)=1−H2(q) and derive expressions for the switched channel capacity under simple parameter choices (e.g., p=q).
• Relate the findings to known literature on causal non-separability and the quantum SWITCH.

Experimental results

Research questions

• RQ1 Can placing two noisy quantum channels in a superposition of causal orders increase the amount of quantum information transmitted compared to definite causal order?
• RQ2 Is heralded noiseless quantum communication possible through channels that are completely dephasing when used in a definite order?
• RQ3 Under what parameter regimes does the switched channel’s coherent information exceed the capacities of the individual channels?
• RQ4 How does the quantum SWITCH affect the bottleneck inequality for quantum communication?
• RQ5 What is the relationship between causal non-separability and practical quantum communication protocols (e.g., BB84, E91)?

Key findings

• Two completely dephasing channels in a quantum SWITCH yield a 25% heralded noiseless transmission probability for p=q=1/2.
• For partially dephasing channels, the switched configuration can deterministically yield a larger quantum capacity than either channel individually.
• The coherent information of the switched channel can exceed the capacities of the individual channels for p values starting around 0.62, indicating a definite advantage of indefinite causal order in that regime.
• The switch can violate the bottleneck inequality, making the switched channel's capacity larger than the capacity of any fixed order composition of the two channels.
• The advantage arises from correlations between the two elementary processes when traversed in superposed orders, enabling information transfer even when each channel blocks quantum information in isolation.