Distributed Compression and Squashed Entanglement

A single quantum state can be shared by many distant parties. In this thesis, we try to characterize the information contents of such distributed states by defining the multiparty information and the multiparty squashed entanglement, two steps toward a general theory of multiparty quantum information. As a further step in that direction, we partially solve the multiparty distributed compression problem where multiple parties use quantum communication to faithfully transfer their shares of a state to a common receiver. We build a protocol for multiparty distributed compression based on the fully quantum Slepian-Wolf protocol and prove both inner and outer bounds on the achievable rate region. We relate our findings to previous results in information theory and discuss some possible applications.Comment: M.Sc thesis submitted to the Physics department of McGill University, 107 pages, 14 figure

Multicasting Homogeneous and Heterogeneous Quantum States in Quantum Networks

In this paper, we target the practical implementation issues of quantum multicast networks. First, we design a recursive lossless compression that allows us to control the trade-off between the circuit complexity and the dimension of the compressed quantum state. We give a formula that describes the trade-off, and further analyze how the formula is affected by the controlling parameter of the recursive procedure. Our recursive lossless compression can be applied in a quantum multicast network where the source outputs homogeneous quantum states (many copies of a quantum state) to a set of destinations through a bottleneck. Such a recursive lossless compression is extremely useful in the current situation where the technology of producing large-scale quantum circuits is limited. Second, we develop two lossless compression schemes that work for heterogeneous quantum states (many copies of a set of quantum states) when the set of quantum states satisfies a certain structure. The heterogeneous compression schemes provide extra compressing power over the homogeneous compression scheme. Finally, we realize our heterogeneous compression schemes in several quantum multicast networks, including the single-source multi-terminal model, the multi-source multi-terminal model, and the ring networks. We then analyze the bandwidth requirements for these network models.Comment: 24 pages, 9 figure

A father protocol for quantum broadcast channels

A new protocol for quantum broadcast channels based on the fully quantum Slepian-Wolf protocol is presented. The protocol yields an achievable rate region for entanglement-assisted transmission of quantum information through a quantum broadcast channel that can be considered the quantum analogue of Marton's region for classical broadcast channels. The protocol can be adapted to yield achievable rate regions for unassisted quantum communication and for entanglement-assisted classical communication; in the case of unassisted transmission, the region we obtain has no independent constraint on the sum rate, only on the individual transmission rates. Regularized versions of all three rate regions are provably optimal.Comment: Typo in statement of Theorem 4 fixe

Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation

We provide several applications of a previously introduced isomorphism between physical operations acting on two systems and entangled states [1]. We show: (i) how to implement (weakly) non-local two qubit unitary operations with a small amount of entanglement; (ii) that a known, noisy, non-local unitary operation as well as an unknown, noisy, local unitary operation can be purified; (iii) how to perform the tomography of arbitrary, unknown, non-local operations; (iv) that a set of local unitary operations as well as a set of non-local unitary operations can be stored and compressed; (v) how to implement probabilistically two-qubit gates for photons. We also show how to compress a set of bipartite entangled states locally, as well as how to implement certain non-local measurements using a small amount of entanglement. Finally, we generalize some of our results to multiparty systems.Comment: 15 pages, no figure

The mother of all protocols: Restructuring quantum information's family tree

We give a simple, direct proof of the "mother" protocol of quantum information theory. In this new formulation, it is easy to see that the mother, or rather her generalization to the fully quantum Slepian-Wolf protocol, simultaneously accomplishes two goals: quantum communication-assisted entanglement distillation, and state transfer from the sender to the receiver. As a result, in addition to her other "children," the mother protocol generates the state merging primitive of Horodecki, Oppenheim and Winter, a fully quantum reverse Shannon theorem, and a new class of distributed compression protocols for correlated quantum sources which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the so-called "father" protocol whose children provide the quantum capacity and the entanglement-assisted capacity of a quantum channel, demonstrating that the division of single-sender/single-receiver protocols into two families was unnecessary: all protocols in the family are children of the mother.Comment: 25 pages, 6 figure