Bound entanglement in measurement based quantum computation

Hans J. Briegel, Dan E. Browne, Wolfgang Dür +2 more

David T. Stephen, Michael Foss-Feig

In measurement-based quantum computation (MBQC), quantum circuits are implemented using adaptive measurements on an entangled resource state. In practice, the resource state will always be prepared with some noise, and it is crucial to understand the effect of this noise on the operation of MBQC. Typically, one measures the fidelity of the noisy resource state with the assumption that a high fidelity state means a high fidelity computation. However, the precise relationship between these two fidelities is not known. Here, we derive an expression that equates the average fidelity of the MBQC output state to a certain correlation function evaluated on the noisy resource state. Using this expression, we show that state fidelity provides a tight lower bound on average MBQC fidelity. Conversely, we also find that state fidelity can greatly underestimate average MBQC fidelity, implying that state fidelity is not a good indicator of MBQC performance in general. In response, we formulate an efficient method to directly estimate average MBQC fidelity by measuring the aforementioned correlation function. These results therefore improve our ability to characterize noisy resource states in quantum computers and benchmark MBQC performance.

István Márton, Erika Bene, Tamás Vértesi

Abstract We present a class of linear correlation witnesses that detects bound entanglement within a three-party prepare-and-measure scenario with four-dimensional quantum messages. We relate the detection power of our witnesses for two-ququart Bloch-product-diagonal states to that of the computable cross norm-realignment criterion. Several bound entangled states in four or even higher dimensions, including those which are useful in metrology, can exceed the separable bound computed by reliable iterative methods. In particular, we show that a prominent two-ququart bound entangled state with a positive partial transpose can be mixed with up to 40% isotropic noise and still be detected as entangled by our prepare-and-measure witness. Furthermore, our witnesses appear to be experimentally practical, requiring only the use of qubit rotations on Alice’s and Bob’s sides and product qubit measurements with binary outcomes on Charlie’s side.

Alba Cervera-Lierta

Jonathan Lavoie

This thesis describes experimental generation, manipulation and measurement of quantum information using photon pairs emitted in bulk crystals. Multi-photon sources engineered during the course of this thesis have proven to be ideal for original contributions in the field of optical quantum information. \n \nIn the first part of this dissertation, we study nonlocality, bound entanglement and measurement-based quantum computing using entangled resources produced by our source. First, we produced and characterised three-photon GHZ polarisation states. We then experimentally violate the long-standing Svetlichny's inequality with a value of 4.51, which is greater than the classical bound by 3.6 standard deviations. Our results agree with the predictions of quantum mechanics, rule out nonlocal hidden-variable theories and certify the genuine tripartite entanglement achievable by our source. Second, with four-photon polarisation states, we demonstrate bound entanglement in Smolin states and realize all of their conceptually important characteristics. Our results highlight the difficulties to achieve the critical condition of undistillability without completely losing entanglement. We conclude the first part by simulating, for the first time, valence-bond solid states and use them as a resource for measurement-based quantum computing. Affleck-Kennedy-Lieb-Tasaki states are produced with 87% fidelity and single-qubit quantum logic gates reach an average fidelity of 92% over all input states and rotations. \n \nIn the second part of this dissertation, we explore controlled waveform manipulation at the single-photon level. Specifically, we shrink the spectral bandwidth of a single photon from 1740 GHz to 43 GHz and demonstrate tunability over a range 70 times that bandwidth. The results are a considerable addition to the field of quantum frequency conversion and have genuine potential for technological applications.

F.J. Duarte