John Paul Barjaktarevic

arXiv2007

Fidelity and quantum phase transitions

It is shown that the fidelity, a basic notion of quantum information science, may be used to characterize quantum phase transitions, regardless of what type of internal order is present in quantum many-body states. If the fidelity of two given states vanishes, then there are two cases: (1) they are in the same phase if the distinguishability results from irrelevant local information; or (2) they are in different phases if the distinguishability results from relevant long-distance information. The different effects of irrelevant and relevant information are quantified, which allows us to identify unstable and stable fixed points (in the sense of renormalization group theory). A physical implication of our results is the occurrence of the orthogonality catastrophe near the transition points.

cond-mat.stat-mech↗

arXiv2005

Teleportation via multi-qubit channels

We investigate the problem of teleporting an unknown qubit state to a recipient via a channel of $2Ł$ qubits. In this procedure a protocol is employed whereby $Ł$ Bell state measurements are made and information based on these measurements is sent via a classical channel to the recipient. Upon receiving this information the recipient determines a local gate which is used to recover the original state. We find that the $2^{2Ł}$-dimensional Hilbert space of states available for the channel admits a decomposition into four subspaces. Every state within a given subspace is a perfect channel, and each sequence of Bell measurements projects $2Ł$ qubits of the system into one of the four subspaces. As a result, only two bits of classical information need be sent to the recipient for them to determine the gate. We note some connections between these four subspaces and ground states of many-body Hamiltonian systems, and discuss the implications of these results towards understanding entanglement in multi-qubit systems.

quant-ph↗