## Publications

133 results found

Rudolph T, Virmani SS, 2023, The two-qubit singlet/triplet measurement is universal for quantum computing given only maximally-mixed initial states, *Nature Communications*, Vol: 14, ISSN: 2041-1723

In order to delineate which minimalistic physical primitives can enable the full power of universal quantum computing, it has been fruitful to consider various measurement based architectures which reduce or eliminate the use of coherent unitary evolution, and also involve operations that are physically natural. In this context previous works had shown that the triplet-singlet measurement of two qubit angular momentum (or equivalently two qubit exchange symmetry) yields the power of quantum computation given access to a few additional different single qubit states or gates. However, Freedman, Hastings and Shokrian-Zini1 recently proposed a remarkable conjecture, called the ‘STP=BQP’ conjecture, which states that the two-qubit singlet/triplet measurement is quantum computationally universal given only an initial ensemble of maximally mixed single qubits. In this work we prove this conjecture. This provides a method for quantum computing that is fully rotationally symmetric (i.e. reference frame independent), using primitives that are physically very-accessible, naturally resilient to certain forms of error, and provably the simplest possible.

Gimeno-Segovia M, Rudolph T, Economou SE, 2019, Deterministic Generation of Large-Scale Entangled Photonic Cluster State from Interacting Solid State Emitters, *PHYSICAL REVIEW LETTERS*, Vol: 123, ISSN: 0031-9007

Morley-Short S, Gimeno-Segovia M, Rudolph T,
et al., 2019, Loss-tolerant teleportation on large stabilizer states, *QUANTUM SCIENCE AND TECHNOLOGY*, Vol: 4, ISSN: 2058-9565

Patel RB, Rudolph T, Pryde GJ, 2019, An experimental quantum Bernoulli factory, *Science Advances*, Vol: 5, Pages: 1-6, ISSN: 2375-2548

There has been a concerted effort to identify problems computable with quantum technology which are intractable with classical technology or require far fewer resources to compute. Recently, randomness processing in a Bernoulli factory has been identified as one such task. Here, we report two quantum photonic implementations of a Bernoulli factory, one utilising quantum coherence and single-qubit measurements and the other which uses quantum coherence and entangling measurements of two qubits. We show that the former consumes three orders of magnitude fewer resources than the best known classical method, while entanglement offers a further five-fold reduction. These concepts may provide a means for quantum enhanced-performance in the simulation of stochastic processes and sampling tasks.

Morley-Short S, Bartolucci S, Gimeno-Segovia M,
et al., 2018, Physical-depth architectural requirements for generating universal photonic cluster states, *QUANTUM SCIENCE AND TECHNOLOGY*, Vol: 3, ISSN: 2058-9565

Zhang X, Lee YH, Bell BA, et al., 2017, Experimental demonstration of relative temporal multiplexing, Conference on Lasers and Electro-Optics Europe / European Quantum Electronics Conference (CLEO/Europe-EQEC), Publisher: Institute of Electrical and Electronics Engineers

Interference between single photons lies at the heart of linear optical quantum computing (LOQC). However, the lack of deterministic single photon sources hinders the large-scale experimental demonstration and its practical applications, as the probability to generate N single photons simultaneously (denoted by N-photon hereafter) decreases exponentially with the increasing number of single photon sources [1]. Multiplexing is the leading proposal to overcome this challenge by relocating single photon from different modes to one fixed mode. The theoretical work [2] indicates that the relative time multiplexing (RMUX) scheme could significantly enhance this probability and meanwhile reduce the requirements of multiplexing system, such as switching speed and system complexity. In this paper, RMUX of two heralded single photon sources is demonstrated for the first time. We observe around 90% enhancement on the heralded photon pair rate, compared to the standard time multiplexing (SMUX) scheme [3].

Zhang X, Lee YH, Bell BA,
et al., 2017, Indistinguishable heralded single photon generation via relative temporal multiplexing of two sources, *Optics Express*, Vol: 25, Pages: 26067-26075, ISSN: 1094-4087

Generating N single photons simultaneously is a formidable challenge due to the lack of deterministic single photon sources. Recent work [New J. Phys. 19, 063013 (2017] has proposed a relative multiplexing scheme that can enhance the N single photons probability with a minimum of active switching resources. We experimentally demonstrate relative temporal multiplexing on two photon sources with a 90% additional enhancement over the standard temporal multiplexing scheme demonstrated previously. 88 ± 11% visibility of Hong-Ou-Mandel quantum interference verifies the indistinguishability of the heralded single photons after the synchronization. This proof-of-principle demonstration points out the potential significance of the relative multiplexing scheme for large-scale photonic quantum information processing.

Gimeno-Segovia M, Cable H, Mendoza GJ,
et al., 2017, Relative multiplexing for minimising switching in linear-optical quantum computing, *NEW JOURNAL OF PHYSICS*, Vol: 19, ISSN: 1367-2630

Nutz TCB, Milne A, Shadbolt P,
et al., 2017, Proposal for demonstration of long-range cluster state entanglement in the presence of photon loss, *APL Photonics*, Vol: 2, ISSN: 2378-0967

Photonic cluster states are a crucial resource for optical quantum computing. Recently a quantum dot single photon source has been demonstrated to produce strings of single photons in a small linear cluster state. Sources of this kind could produce much larger cluster states, but high photon loss rates make it impossible to characterize the entanglement generated by quantum state tomography. We present a benchmarking method for such sources that can be used to demonstrate useful long-range entanglement with currently available collection/detection efficiencies below 1%. The measurement of the polarization state of single photons in different bases can provide an estimate for the three-qubit correlation function ⟨ZXZ⟩. This value constrains correlations spanning more than three qubits, which in turn provide a lower bound for the localizable entanglement between any two qubits in the large state produced by the source. Finite localizable entanglement can be established by demonstrating ⟨ZXZ⟩>23. This result enables photonic experiments demonstrating computationally useful entanglement with currently available technology.

Lostaglio M, Jennings D, Rudolph T, 2017, Thermodynamic resource theories, non-commutativity and maximum entropy principles, *NEW JOURNAL OF PHYSICS*, Vol: 19, ISSN: 1367-2630

We discuss some features of thermodynamics in the presence of multiple conserved quantities. We prove a generalisation of Landauer principle illustrating tradeoffs between the erasure costs paid in different 'currencies'. We then show how the maximum entropy and complete passivity approaches give different answers in the presence of multiple observables. We discuss how this seems to prevent current resource theories from fully capturing thermodynamic aspects of non-commutativity.

Rudolph T, 2017, Why I am optimistic about the silicon-photonic route to quantum computing, *APL PHOTONICS*, Vol: 2, ISSN: 2378-0967

Simmons A, Wallman J, Pashayan H,
et al., 2017, Contextuality under weak assumptions, *New Journal of Physics*, Vol: 19, ISSN: 1367-2630

The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements could not be viewed as deterministically revealing pre-existing properties of the system. More precisely, no model can assign deterministic outcomes to the projectors of a quantum measurement in a way that depends only on the projector and not the context (the full set of projectors) in which it appeared, despite the fact that the Born rule probabilities associated with projectors are independent of the context. A more general, operational definition of contextuality introduced by Spekkens, which we will term "probabilistic contextuality", drops the assumption of determinism and allows for operations other than measurements to be considered contextual. Even two-dimensional quantum mechanics can be shown to be contextual under this generalised notion. Probabilistic noncontextuality represents the postulate that elements of an operational theory that cannot be distinguished from each other based on the statistics of arbitrarily many repeated experiments (they give rise to the same operational probabilities) are ontologically identical. In this paper, we introduce a framework that enables us to distinguish between different noncontextuality assumptions in terms of the relationships between the ontological representations of objects in the theory given a certain relation between their operational representations. This framework can be used to motivate and define a "possibilistic" analogue, encapsulating the idea that elements of an operational theory that cannot be unambiguously distinguished operationally can also not be unambiguously distinguished ontologically. We then prove that possibilistic noncontextuality is equivalent to an alternative notion of noncontextuality proposed by Hardy. Finally, we demonstrate that these weaker noncontextuality assumptions are sufficien

Alnasser S, Cheema A, Horlick E, et al., 2016, Optimal Transcatheter Heart Valve Sizing in Aortic Valve in Valve Implantation: Insights from the Valve in Valve International Data (VIVID) Registry, 28th Annual Transcatheter Cardiovascular Therapeutics Symposium (TCT), Publisher: ELSEVIER SCIENCE INC, Pages: B271-B271, ISSN: 0735-1097

Frenzel MF, Jennings D, Rudolph T, 2016, Quasi-autonomous quantum thermal machines and quantum to classical energy flow, *New Journal of Physics*, Vol: 18, ISSN: 1367-2630

There are both practical and foundational motivations to consider the thermodynamics of quantumsystems at small scales. Here we address the issue of autonomous quantum thermal machinesthat are tailored to achieve some specific thermodynamic primitive, such as work extraction in thepresence of a thermal environment, while having minimal or no control from the macroscopic regime.Beyond experimental implementations, this provides an arena in which to address certain foundationalaspects such as the role of coherence in thermodynamics, the use of clock degrees of freedomand the simulation of local time-dependent Hamiltonians in a particular quantum subsystem. Forsmall-scale systems additional issues arise. Firstly, it is not clear to what degree genuine orderedthermodynamic work has been extracted, and secondly non-trivial back-actions on the thermal machinemust be accounted for. We find that both these aspects can be resolved through a judiciouschoice of quantum measurements that magnify thermodynamic properties up the ladder of lengthscales,while simultaneously stabilizing the quantum thermal machine. Within this framework weshow that thermodynamic reversibility is obtained in a particular Zeno limit, and finally illustratethese concepts with a concrete example involving spin-systems.

Nigg D, Monz T, Schindler P,
et al., 2015, Can different quantum state vectors correspond to the same physical state? An experimental test, *NEW JOURNAL OF PHYSICS*, Vol: 18, ISSN: 1367-2630

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- Citations: 1

Jevtic S, Jennings D, Rudolph T,
et al., 2015, Exchange Fluctuation Theorem for correlated quantum systems, *Physical Review E*, Vol: 92, Pages: 042113-1-042113-12, ISSN: 1539-3755

We extend the Exchange Fluctuation Theorem for energy exchange betweenthermal quantum systems beyond the assumption of molecular chaos, and describethe non-equilibrium exchange dynamics of correlated quantum states. Therelation quantifies how the tendency for systems to equilibrate is modified inhigh-correlation environments. Our results elucidate the role of measurementdisturbance for such scenarios. We show a simple application by finding asemi-classical maximum work theorem in the presence of correlations.

Goodwin JF, Brown BJ, Stutter G,
et al., 2015, Trapped-ion quantum error-correcting protocols using only global operations, *Physical Review A*, Vol: 92, Pages: 032314-1-032314-7, ISSN: 1094-1622

Quantum error-correcting codes are many-body entangled states used to robustly store coherent quantum statesover long periods of time in the presence of noise. Practical implementations will require efficient entanglingprotocols that minimize the introduction of noise during encoding or readout. We propose an experiment thatuses only global operations to encode information to either the five-qubit repetition code or the five-qubit code ona two-dimensional ion Coulomb crystal architecture. We show we can prepare, read out, and acquire syndromeinformation for these two codes by using only six and ten global entangling pulses, respectively. We provide anerror analysis, estimating we can achieve a sixfold improvement in coherence time with as much as 1% noise inthe control parameters for each entangling operation.

Dale H, Jennings D, Rudolph T, 2015, Provable quantum advantage in randomness processing, *Nature Communications*, Vol: 6, ISSN: 2041-1723

Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics exactly coincides with the class computable quantum mechanically. It is strongly believed, but not proven, that quantum computing provides exponential speed-up for a range of problems, such as factoring. Here we address a computational scenario of randomness processing in which quantum theory provably yields, not only resource reduction over classical stochastic physics, but a strictly larger class of problems which can be solved. Beyond new foundational insights into the nature and malleability of randomness, and the distinction between quantum and classical information, these results also offer the potential of developing classically intractable simulations with currently accessible quantum technologies.

Karanjai A, Cavalcanti EG, Bartlett SD,
et al., 2015, Weak values in a classical theory with an epistemic restriction, *New Journal of Physics*, Vol: 17, ISSN: 1367-2630

Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the procedure of weak measurement and postselection, and the interpretation of the associated weak value, using a theory of classical mechanics supplemented by an epistemic restriction that is known to be operationally equivalent to a subtheory of quantum mechanics. Both the real and imaginary components of the weak value appear as phase space displacements in the postselected expectation values of the measurement device's position and momentum distributions, and we recover the same displacements as in the quantum case by studying the corresponding evolution in our theory of classical mechanics with an epistemic restriction. By using this epistemically restricted theory, we gain insight into the appearance of the weak value as a result of the statistical effects of post selection, and this provides us with an operational interpretation of the weak value, both its real and imaginary parts. We find that the imaginary part of the weak value is a measure of how much postselection biases the mean phase space distribution for a given amount of measurement disturbance. All such biases proportional to the imaginary part of the weak value vanish in the limit where disturbance due to measurement goes to zero. Our analysis also offers intuitive insight into how measurement disturbance can be minimized and the limits of weak measurement.

Milne A, Jennings D, Rudolph T, 2015, Geometric representation of two-qubit entanglement witnesses, *PHYSICAL REVIEW A*, Vol: 92, ISSN: 1050-2947

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- Citations: 11

Gimeno-Segovia M, Shadbolt P, Browne DE,
et al., 2015, From three-photon Greenberger-Horne-Zeilinger states to ballistic universal quantum computation, *Physical Review Letters*, Vol: 115, ISSN: 0031-9007

Single photons, manipulated using integrated linear optics, constitute a promising platform for universal quantum computation. A series of increasingly efficient proposals have shown linear-optical quantum computing to be formally scalable. However, existing schemes typically require extensive adaptive switching, which is experimentally challenging and noisy, thousands of photon sources per renormalized qubit, and/or large quantum memories for repeat-until-success strategies. Our work overcomes all these problems. We present a scheme to construct a cluster state universal for quantum computation, which uses no adaptive switching, no large memories, and which is at least an order of magnitude more resource efficient than previous passive schemes. Unlike previous proposals, it is constructed entirely from loss-detecting gates and offers a robustness to photon loss. Even without the use of an active loss-tolerant encoding, our scheme naturally tolerates a total loss rate ∼1.6% in the photons detected in the gates. This scheme uses only 3 Greenberger-Horne-Zeilinger states as a resource, together with a passive linear-optical network. We fully describe and model the iterative process of cluster generation, including photon loss and gate failure. This demonstrates that building a linear-optical quantum computer needs to be less challenging than previously thought.

Lostaglio M, Korzekwa K, Jennings D,
et al., 2015, Quantum coherence, time-translation symmetry, and thermodynamics, *Physical Review X*, Vol: 5, ISSN: 2160-3308

The first law of thermodynamics imposes not just a constraint on the energy content of systems in extreme quantum regimes but also symmetry constraints related to the thermodynamic processing of quantum coherence. We show that this thermodynamic symmetry decomposes any quantum state into mode operators that quantify the coherence present in the state. We then establish general upper and lower bounds for the evolution of quantum coherence under arbitrary thermal operations, valid for any temperature. We identify primitive coherence manipulations and show that the transfer of coherence between energy levels manifests irreversibility not captured by free energy. Moreover, the recently developed thermomajorization relations on block-diagonal quantum states are observed to be special cases of this symmetry analysis.

Zaidi HA, Dawson C, van Loock P,
et al., 2015, Near-deterministic creation of universal cluster states with probabilistic Bell measurements and three-qubit resource states, *PHYSICAL REVIEW A*, Vol: 91, ISSN: 1050-2947

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- Citations: 17

Jevtic S, Rudolph T, 2015, How Einstein and/or Schrodinger should have discovered Bell's theorem in 1936, *JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS*, Vol: 32, Pages: A50-A55, ISSN: 0740-3224

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- Citations: 3

Lostaglio R, Jennings D, Rudolph T, 2015, Description of quantum coherence in thermodynamic processes requires constraints beyond free energy, *Nature Communications*, Vol: 6, ISSN: 2041-1723

Recent studies have developed fundamental limitations on nanoscale thermodynamics, in terms of a set of independent free energy relations. Here we show that free energy relations cannot properly describe quantum coherence in thermodynamic processes. By casting time-asymmetry as a quantifiable, fundamental resource of a quantum state, we arrive at an additional, independent set of thermodynamic constraints that naturally extend the existing ones. These asymmetry relations reveal that the traditional Szilárd engine argument does not extend automatically to quantum coherences, but instead only relational coherences in a multipartite scenario can contribute to thermodynamic work. We find that coherence transformations are always irreversible. Our results also reveal additional structural parallels between thermodynamics and the theory of entanglement.

Jevtic S, Newman D, Rudolph T,
et al., 2015, Single-qubit thermometry, *PHYSICAL REVIEW A*, Vol: 91, ISSN: 1050-2947

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- Citations: 60

McCutcheon DPS, Lindner NH, Rudolph T, 2014, Error Distributions on Large Entangled States with Non-Markovian Dynamics, *PHYSICAL REVIEW LETTERS*, Vol: 113, ISSN: 0031-9007

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- Citations: 10

Frenzel MF, Jennings D, Rudolph T, 2014, Reexamination of pure qubit work extraction, *Physical Review E*, Vol: 90, ISSN: 1539-3755

Many work extraction or information erasure processes in the literature involve the raising and loweringof energy levels via external fields. But even if the actual system is treated quantum mechanically, the fieldis assumed to be classical and of infinite strength, hence not developing any correlations with the system orexperiencing back-actions. We extend these considerations to a fully quantum mechanical treatment by studyinga spin-1/2 particle coupled to a finite-sized directional quantum reference frame, a spin-l system, which modelsan external field. With this concrete model together with a bosonic thermal bath, we analyze the back-actiona finite-size field suffers during a quantum-mechanical work extraction process and the effect this has on theextractable work and highlight a range of assumptions commonly made when considering such processes. Thewell-known semiclassical treatment of work extraction from a pure qubit predicts a maximum extractable workW = kT log 2 for a quasistatic process, which holds as a strict upper bound in the fully quantum mechanical caseand is attained only in the classical limit. We also address the problem of emergent local time dependence in ajoint system with a globally fixed Hamiltonian.

Lund AP, Laing A, Rahimi-Keshari S,
et al., 2014, Boson Sampling from a Gaussian State, *PHYSICAL REVIEW LETTERS*, Vol: 113, ISSN: 0031-9007

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- Citations: 173

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