249 research outputs found
Entanglement and quantum combinatorial designs
We introduce several classes of quantum combinatorial designs, namely quantum
Latin squares, cubes, hypercubes and a notion of orthogonality between them. A
further introduced notion, quantum orthogonal arrays, generalizes all previous
classes of designs. We show that mutually orthogonal quantum Latin arrangements
can be entangled in the same way than quantum states are entangled.
Furthermore, we show that such designs naturally define a remarkable class of
genuinely multipartite highly entangled states called -uniform, i.e.
multipartite pure states such that every reduction to parties is maximally
mixed. We derive infinitely many classes of mutually orthogonal quantum Latin
arrangements and quantum orthogonal arrays having an arbitrary large number of
columns. The corresponding multipartite -uniform states exhibit a high
persistency of entanglement, which makes them ideal candidates to develop
multipartite quantum information protocols.Comment: 14 pages, 3 figures. Comments are very welcome
Holonomy for Quantum Channels
A quantum holonomy reflects the curvature of some underlying structure of
quantum mechanical systems, such as that associated with quantum states. Here,
we extend the notion of holonomy to families of quantum channels, i.e., trace
preserving completely positive maps. By the use of the Jamio{\l}kowski
isomorphism, we show that the proposed channel holonomy is related to the
Uhlmann holonomy. The general theory is illustrated for specific examples. We
put forward a physical realization of the channel holonomy in terms of
interferometry. This enables us to identify a gauge invariant physical object
that directly relates to the channel holonomy. Parallel transport condition and
concomitant gauge structure are delineated in the case of smoothly parametrized
families of channels. Finally, we point out that interferometer tests that have
been carried out in the past to confirm the rotation symmetry of the
neutron spin, can be viewed as early experimental realizations of the channel
holonomy.Comment: Minor changes, journal reference adde
Holographic duality from random tensor networks
Tensor networks provide a natural framework for exploring holographic duality
because they obey entanglement area laws. They have been used to construct
explicit toy models realizing many interesting structural features of the
AdS/CFT correspondence, including the non-uniqueness of bulk operator
reconstruction in the boundary theory. In this article, we explore the
holographic properties of networks of random tensors. We find that our models
naturally incorporate many features that are analogous to those of the AdS/CFT
correspondence. When the bond dimension of the tensors is large, we show that
the entanglement entropy of boundary regions, whether connected or not, obey
the Ryu-Takayanagi entropy formula, a fact closely related to known properties
of the multipartite entanglement of assistance. Moreover, we find that each
boundary region faithfully encodes the physics of the entire bulk entanglement
wedge. Our method is to interpret the average over random tensors as the
partition function of a classical ferromagnetic Ising model, so that the
minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the
analog of a bulk field, we find that our model reproduces the expected
corrections to the Ryu-Takayanagi formula: the minimal surface is displaced and
the entropy is augmented by the entanglement of the bulk field. Increasing the
entanglement of the bulk field ultimately changes the minimal surface
topologically in a way similar to creation of a black hole. Extrapolating bulk
correlation functions to the boundary permits the calculation of the scaling
dimensions of boundary operators, which exhibit a large gap between a small
number of low-dimension operators and the rest. While we are primarily
motivated by AdS/CFT duality, our main results define a more general form of
bulk-boundary correspondence which could be useful for extending holography to
other spacetimes.Comment: 57 pages, 13 figure
Deterministic generation of qudit photonic graph states from quantum emitters
We propose and analyze deterministic protocols to generate qudit photonic
graph states from quantum emitters. We exemplify our approach by constructing
protocols to generate absolutely maximally entangled states and logical states
of quantum error correcting codes. Some of these protocols make use of
time-delayed feedback, while others do not. These results significantly broaden
the range of multi-photon entangled states that can be produced
deterministically from quantum emitters.Comment: 14 pages, 5 figure
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