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Laura Mancinska and David Roberson visiting
Laura Mancinska and David Roberson visiting
1st March 2019  6th March 2019 @
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QIT Seminar  Laura Mancinska (Copenhagen)  Quantum majority and other basis independent functions
QIT Seminar  Laura Mancinska (Copenhagen)  Quantum majority and other basis independent functions
1st March 2019 @ 12:00  13:00
We consider a version of delegated computation scenario where the input data is scrambled by an unknown unitary. Specifically, we look at a task where, upon receiving a quantum state U^{\otimes n} \ket{x} Bob aims to output U \ket{f(x)}; here x is an unknown bit string, U is an unknown qubit unitary and f is a (known) Boolean function. We will discuss our motivation and optimal quantum protocols for it. Within this rather general framework we will closer examine the case, where f is the majority function. Our proof techniques involve SchurWeyl duality and representation theory of the unitary group.
This is an ongoing joint work with Harry Buhrman, Noah Linden, Ashley Montanaro, and Maris Ozols.
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Laura Mancinska and David Roberson visiting
Laura Mancinska and David Roberson visiting
1st March 2019  6th March 2019 @
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Laura Mancinska and David Roberson visiting
Laura Mancinska and David Roberson visiting
1st March 2019  6th March 2019 @
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Laura Mancinska and David Roberson visiting
Laura Mancinska and David Roberson visiting
1st March 2019  6th March 2019 @
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Laura Mancinska and David Roberson visiting
Laura Mancinska and David Roberson visiting
1st March 2019  6th March 2019 @
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Laura Mancinska and David Roberson visiting
Laura Mancinska and David Roberson visiting
1st March 2019  6th March 2019 @
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QIT Seminar  David Roberson (Copenhagen)  Quantum isomorphisms, quantum groups, and counting homomorphisms
QIT Seminar  David Roberson (Copenhagen)  Quantum isomorphisms, quantum groups, and counting homomorphisms
6th March 2019 @ 16:00  17:00
SM3 (Maths)
I will present a connection between quantum information and quantum permutation groups provided by quantum strategies for the socalled graph isomorphism game. I will start by defining the isomorphism game and its quantum strategies as prescribed by two potentially different models: the tensor product model and the commuting model. We will see that the existence of a commuting strategy can naturally be expressed in the language of quantum groups. Specifically, we will see that that two connected graphs X and Y are quantum (commuting) isomorphic if and only if there exists x \in V(X) and y \in V(Y) that are in the same orbit of the quantum automorphism group of the disjoint union of X and Y. This connection links quantum groups to the more concrete notion of nonlocal games and physically observable quantum behaviors. We will also define orbitals (orbits on ordered pairs) of the quantum automorphism group of a graph, and see that they form a coherent configuration/algebra, a well studied concept from algebraic graph theory. If time permits, we will also discuss a new result that characterizes quantum isomorphism in terms of counting (classical) homomorphisms from planar graphs.
This talk is based on arXiv:1611.09837, arXiv:1712.01820, and new work with Laura Mančinska.
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QIT Seminar  Zixin Huang (Sheffield)  Quantum metrology, quantum cryptography, and everything in between
QIT Seminar  Zixin Huang (Sheffield)  Quantum metrology, quantum cryptography, and everything in between
13th March 2019 @ 16:00  17:00
Room F40, Biomedical Sciences
I will discuss a general framework for parameter estimation that allows only trusted parties to access the result and achieves optimal precision. The protocols are designed such that adversaries can access some information indeterministically, but only at the risk of getting caught (cheatsensitivity). By combining techniques from quantum cryptography and quantum metrology, we devise cryptographic procedures for single parameter estimation when an arbitrary number of parties are involved. [1]
For phase estimation, we show that for Gaussian states, an ancillaassisted scheme outperforms the classical strategy for all levels of loss. We find the optimal measurement observable for each scheme discussed. We also find that with the appropriate measurement, the achievable precision of the proposal by Caves [Phys. Rev. D 23, 1693] can be improved upon, and is less vulnerable to losses than previously thought. [2]
Lastly, I will discuss a quantum privatekey encryption protocol inspired by Boson Sampling. While Boson Sampling is classically hard to simulate, here we show that its cryptographic application is hard also for a quantum computer.
[1] Cryptographic quantum metrology Physical Review A 99 (2), 022314
[2] Losstolerant and ancillaassisted Gaussian state quantum metrology arXiv:1811.10554
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QIT Seminar  Tamara Köhler (UCL)  Complete Toy Models of Holographic Duality
QIT Seminar  Tamara Köhler (UCL)  Complete Toy Models of Holographic Duality
27th March 2019 @ 16:00  17:00
SM3
This talk will discuss recent work applying quantum information theory techniques to construct toy models of the AdS/CFT correspondence. The AdS/CFT correspondence is a conjectured duality between quantum gravity in (d+1) dimensional asymptotically AdS space, and a conformal field theory defined on its boundary. It has recently been pointed out that the emergence of bulk locality in AdS/CFT can be characterised in terms of quantum error correcting codes. This has led to the construction of holographic quantum error correcting codes (HQECC) which are toy models of the duality. However, HQECC do not map local bulk Hamiltonians to local Hamiltonians on the boundary, so do not give a duality between bulk and boundary energy scales or dynamics. In this work, we combine HQECC with Hamiltonian simulation theory to construct a bulkboundary mapping between local Hamiltonians. This allows us to construct a toy model of holographic duality between models, encompassing the relationship between bulk and boundary energy scales and time dynamics.
It also allows us to construct a map in the reverse direction: from local boundary Hamiltonians to the corresponding Hamiltonian in the bulk. Under this boundarytobulk mapping the bulk geometry emerges as an approximate lowenergy effective theory living in the code space of an (approximate) HQECC on the boundary. At higher energy slices this emergent bulk geometry is modified in a way that matches the toy models of black holes proposed previously for HQECC. Moreover, the duality on the level of dynamics shows how these toymodel black holes can form dynamically.
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