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New Hub Paper: ‘Limitations of entropic inequalities for detecting nonclassicality in the postselected Bell causal structure’




V. Vilasini and Roger Colbeck (2020). Limitations of entropic inequalities for detecting nonclassicality in the postselected Bell causal structure, Phys. Rev. Research, 2, 033096, 10.1103/PhysRevResearch.2.033096.

Classical and quantum physics impose different constraints on the joint probability distributions of observed variables in a causal structure. These differences mean that certain correlations can be certified as nonclassical, which has both foundational and practical importance. Rather than working with the probability distribution itself, it can instead be convenient to work with the entropies of the observed variables. In the Bell causal structure with two inputs and outputs per party, a technique that uses entropic inequalities is known that can always identify nonclassical correlations. Here we consider the analog of this technique in the generalization of this scenario to more outcomes. We identify a family of nonclassical correlations in the Bell scenario with two inputs and three outputs per party whose nonclassicality cannot be detected through the direct analog of the previous technique. We also show that use of Tsallis entropy instead of Shannon entropy does not help in this case. Furthermore, we give evidence that natural extensions of the technique also do not help. More precisely, our evidence suggests that even if we allow the observed correlations to be postprocessed according to a natural class of nonclassicality nongenerating operations, entropic inequalities for either the Shannon or Tsallis entropies cannot detect the nonclassicality, and hence that entropic inequalities are generally not sufficient to detect nonclassicality in the Bell causal structure.

In addition, for the bipartite Bell scenario with two inputs and three outputs we find the vertex description of the polytope of nonsignalling distributions that satisfy all of the CHSH-type inequalities, which is one of the main regions of investigation in this work.



Hub job opportunity!




University of Cambridge

The Department of Engineering, University of Cambridge, seeks to appoint a Research Associate to work on Quantum Communications as part of the Quantum Communications Hub, until 30 November 2022, extendable for another 2 years.

The post holder will be located in the Electrical Engineering Building on the West Cambridge Site, Cambridge, UK.

The key responsibilities and duties are to maintain the network and introduce new systems for trial. This will involve design, construction and assessment of sub-systems. Examples of tests are the hybrid Continuous Variable (CV) QKD system, the new Quantum Alarm, and options for carrying out signal processing using CV techniques. Preference will be given to candidates with demonstrated quantum or photonic communications experimental aptitude in relevant areas of research and an ability to work within a team. Experience of DSP/FPGA programming would be an advantage.

The qualifications required to perform the role are to have obtained a PhD in Electronic Engineering, Physics, Applied Maths, Computer Science, or a related discipline. A good publication record would be an advantage.

Salary Ranges: Research Associate: £32,816 – £40,322

Fixed-term: The funds for this post are available until 30 November 2022 in the first instance.

For more information regarding this position follow this link.


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Quantum Algorithms for Simulating the Lattice Schwinger Model




Alexander F. Shaw1,5, Pavel Lougovski1, Jesse R. Stryker2, and Nathan Wiebe3,4

1Quantum Information Science Group, Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S.A.
2Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550, U.S.A.
3Department of Physics, University of Washington, Seattle, WA 98195, U.S.A.
4Pacific Northwest National Laboratory, Richland, WA 99354, U.S.A.
5Department of Physics, University of Maryland, College Park, Maryland 20742, U.S.A.

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The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In particular, we perform a tight analysis of low-order Trotter formula simulations of the Schwinger model, using recently derived commutator bounds, and give upper bounds on the resources needed for simulations in both scenarios. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x^{-1/2}$ and electric field cutoff $x^{-1/2}Lambda$ can be simulated on a quantum computer for time $2xT$ using a number of $T$-gates or CNOTs in $widetilde{O}( N^{3/2} T^{3/2} sqrt{x} Lambda )$ for fixed operator error. This scaling with the truncation $Lambda$ is better than that expected from algorithms such as qubitization or QDRIFT. Furthermore, we give scalable measurement schemes and algorithms to estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable–the mean pair density. Finally, we bound the root-mean-square error in estimating this observable via simulation as a function of the diamond distance between the ideal and actual CNOT channels. This work provides a rigorous analysis of simulating the Schwinger model, while also providing benchmarks against which subsequent simulation algorithms can be tested.

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Cited by

[1] Indrakshi Raychowdhury and Jesse R. Stryker, “Solving Gauss’s Law on Digital Quantum Computers with Loop-String-Hadron Digitization”, arXiv:1812.07554.

[2] Christopher David White, ChunJun Cao, and Brian Swingle, “Conformal field theories are magical”, arXiv:2007.01303.

[3] Anthony Ciavarella, “An Algorithm for Quantum Computation of Particle Decays”, arXiv:2007.04447.

[4] Minh C. Tran, Yuan Su, Daniel Carney, and Jacob M. Taylor, “Faster Digital Quantum Simulation by Symmetry Protection”, arXiv:2006.16248.

The above citations are from SAO/NASA ADS (last updated successfully 2020-08-12 00:44:15). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2020-08-12 00:44:14).


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Mapping graph state orbits under local complementation




Jeremy C. Adcock1, Sam Morley-Short1, Axel Dahlberg2, and Joshua W. Silverstone1

1Quantum Engineering Technology (QET) Labs, H. H. Wills Physics Laboratory & Department of Electrical & Electronic Engineering, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol BS8 1UB, UK
2QuTech – TU Delft, Lorentzweg 1, 2628CJ Delft, The Netherlands

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Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation – the graph operation that links all local-Clifford equivalent graph states – allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data for each of the $587$ orbits up to $9$ qubits and a means to visualise them. We find direct links between the connectivity of certain orbits with the entanglement properties of their component graph states. Furthermore, we observe the correlations between graph-theoretical orbit properties, such as diameter and colourability, with Schmidt measure and preparation complexity and suggest potential applications. It is well known that graph theory and quantum entanglement have strong interplay – our exploration deepens this relationship, providing new tools with which to probe the nature of entanglement.

Graph states are ubiquitous representations of entanglement in quantum information science, and classify the most studied set of quantum states—clifford states—by the entanglement they possess.

However, many graph states are locally equivalent to one another, that is, they possess the same type of entanglement. Graph states which are locally equivalent can be transformed into one another by successive applications of the graph operation local complementation (example shown above). Using this operation, we can analyse only graph structure of the state, which is much simpler than analysing the exponentially large quantum state vector. This equivalence of graph states has been studied previously, with all graph states up to 12 qubits classified.

However, local complementation gives us more than sets of locally equivalent graphs: it also gives us an orbit (example shown above) which tells us how different graphs are related via local complementation. In this work we study these orbits, and relate their properties to properties of the entangled quantum states they contain. We find that orbit properties, such as colourability, correlate with entanglement properties, such as schmidt measure, and discuss applications of local complementation in quantum technology.

► BibTeX data

► References

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