Year: 2012
Type: article
Abstract: If a quantum system is subject to noise, it is possible to perform quantum error correction reversing the action of the noise if and only if no information about the system's quantum state leaks to the environment. In this paper, we develop an analogous duality in the case that the environment approximately forgets the identity of the quantum state, a weaker condition satisfied by -randomizing maps and approximate unitary designs. Specifically, we show that the environment approximately forgets quantum states if and only if the original channel approximately preserves pairwise fidelities of pure inputs, an observation we call weak decoupling duality. Using this tool, we then go on to study the task of using the output of a channel to simulate restricted classes of measurements on a space of input states. The case of simulating measurements that test whether the input state is an arbitrary pure state is known as equality testing or quantum identification. An immediate consequence of weak decoupling duality is that the ability to perform quantum identification cannot be cloned. We, furthermore, establish that the optimal amortized rate at which quantum states can be identified through a noisy quantum channel is equal to the entanglement-assisted classical capacity of the channel, despite the fact that the task is quantum, not classical, and entanglement-assistance is not allowed. In particular, this rate is strictly positive for every nonconstant quantum channel, including classical channels.
Authors: Patrick Hayden, Andreas Winter
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: Canadian Institute for Advanced Research, Leverhulme Trust, European Commission, National Research Foundation, Canada Research Chairs, Fonds Québécois de la Recherche sur la Nature et les Technologies, Mitacs, Centre for Quantum Technologies, Institut Périmètre de physique théorique, Natural Sciences and Engineering Research Council of Canada, Engineering and Physical Sciences Research Council, Office of Naval Research
Award: G6802888625
OpenAlex ID: W2050047129