New Approach to Quantify Quantum Memory Using Channel Ellipsoids

Quantum memory, a key component in quantum information science, can now be quantified and detected using a new approach based on the concept of channel ellipsoids. This method, which does not rely on presumptions about input quantum states, allows for the visual characterization of single-qubit quantum memory. The approach is applicable in both Markovian and non-Markovian scenarios, making it a significant advancement in the understanding and application of quantum memory. This could have major implications for tasks such as entanglement-based quantum key distribution, quantum communication, and quantum teleportation.

What is Quantum Memory and Why is it Important?

Quantum memory is a critical component in the field of quantum information science. It plays a central role in storing quantum information, which is a fundamental requirement for the operation of a quantum network. The minimal criterion for a reliable quantum memory is the maintenance of the entangled state, which can be described by the non-entanglement-breaking (non-EB) channel.

Quantum memory is essential for various quantum information tasks based on entangled resources, such as entanglement-based quantum key distribution, quantum communication, and quantum teleportation. These tasks would not be functional if there is an entanglement-breaking quantum memory in the network. Therefore, verifying a functional quantum memory is a crucial task, and several independent protocols have been proposed for this purpose.

How Can Quantum Memory be Quantified?

In a recent study, researchers have proposed a new approach to quantify all single-qubit quantum memories. This approach involves the concept of channel ellipsoids, which are similar to quantum steering ellipsoids used to characterize the entanglement between qubit-qubit systems.

The channel ellipsoid of a single-qubit quantum memory is defined as the set of all output states in the Bloch sphere. Although a channel ellipsoid is defined by all output states, the geometrical data are accessible with a finite number of inputs, which is useful for experimental studies on quantum memories.

This approach does not presume on the input quantum states, meaning that one can construct the channel ellipsoids of a single-qubit quantum memory in a semi-device-independent scenario.

What is the Significance of the Channel Ellipsoid?

The geometric data from the channel ellipsoid can reconstruct the quantum channel in the Choi-Jamiołkowski (CJ) representation. Therefore, all the properties of the single-qubit quantum memory can be visually characterized by the channel ellipsoid.

The volume of the channel ellipsoid provides a clear physical interpretation of the quantification of the quantum memory. Moreover, the geometrical representations of EB channels with channel ellipsoids provide a simple metric for quantifying a quantum memory in terms of its volume.

How Can Quantum Memory be Detected?

To illustrate the approach of detecting quantum memory, the researchers considered several examples of Markovian dynamics such as the depolarizing and amplitude damping channels with constant rates. They also utilized IBM quantum simulation to demonstrate the ellipsoids in the two cases mentioned above.

The researchers found that their approach also functions for a highly symmetric non-Markovian scenario. This finding suggests that the approach could be widely applicable in the field of quantum information science.

What are the Implications of this Research?

This research provides a new approach to quantify and detect quantum memory, which is a critical component in the field of quantum information science. The approach is based on the concept of channel ellipsoids and does not presume on the input quantum states, making it useful for experimental studies on quantum memories.

The findings of this research could have significant implications for various quantum information tasks based on entangled resources, such as entanglement-based quantum key distribution, quantum communication, and quantum teleportation.

Moreover, the approach could be widely applicable in the field of quantum information science, as it functions for both Markovian and non-Markovian scenarios. This research represents a significant step forward in the understanding and application of quantum memory.