Annals of physics

In this paper, we introduce a general framework to study the concept of robust self-testing which can be used to self-test maximally entangled pairs of qubits (EPR pairs) and local measurement operators. The result is based only on probabilities obtained from the experiment, with tolerance to experimental errors. In particular, we show that if the results of an experiment approach the Cirel'son bound, or approximate the Mayers-Yao-type correlations, then the experiment must contain an approximate EPR pair. More specifically, there exist local bases in which the physical state is close to an EPR pair, possibly encoded in a larger environment or ancilla. Moreover, in these bases the measurements are close to the qubit operators used to achieve the Cirel'son bound or the Mayers-Yao results. © 2012 IOP Publishing Ltd.

https://iopscience.iop.org/article/10.1088/1751-8113/45/45/455304/pdf

Robust self-testing of the singlet

Fortschritte der Physik = Progress of physics

It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error $\epsilon$ in trace distance required $O(dr^2/\epsilon^2)$ copies for a $d$-dimensional density matrix of rank $r$. Here, we give a theoretical measurement scheme (POVM) that requires $O (dr/ \delta ) \ln (d/\delta) $ copies of $\rho$ to error $\delta$ in infidelity, and a matching lower bound up to logarithmic factors. This implies $O( (dr / \epsilon^2) \ln (d/\epsilon) )$ copies suffice to achieve error $\epsilon$ in trace distance. We also prove that for independent (product) measurements, $\Omega(dr^2/\delta^2) / \ln(1/\delta)$ copies are necessary in order to achieve error $\delta$ in infidelity. For fixed $d$, our measurement can be implemented on a quantum computer in time polynomial in $n$.

/pdf/sample-optimal-tomography-of-quantum-states-49ndi8s0bs.pdf

Sample-optimal tomography of quantum states

Hot ice computer

Efficient generation of cluster states is crucial for engineering large-scale measurement-based quantum computers. Hybrid matter-optical systems offer a robust, scalable path to this goal. Such systems have an ancilla which acts as a bus connecting the qubits. We show that by generating the cluster in smaller sections of interlocking bricks, reusing one ancilla per brick, the cluster can be produced with maximal efficiency, requiring fewer than half the operations compared with no bus reuse. By reducing the time required to prepare sections of the cluster, bus reuse more than doubles the size of the computational workspace that can be used before decoherence effects dominate. A row of buses in parallel provides fully scalable cluster-state generation requiring only 20 controlled-phase gates per bus use.

Reduce, reuse, recycle for robust cluster-state generation

We propose schemes to realize two non-standard quantum measurements using cavity quantum electrodynamics (QED). Such measurements have only been realized on photons, and realizations using atoms could be more easily scaled than existing realizations using photons.

Vivien M. Kendon

Papers

Reduce, reuse, recycle for robust cluster-state generation

Quantum measurements of atoms using cavity qed

Theory of Quantum Computation, Communication, and Cryptography

Analogue Computation with Microwaves.

Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography