arXiv subjects

Terry Rudolph

Publications and source records attributed to Terry Rudolph.

At least 55 records · Page 3Linked to original sources

arXiv2014

Near-deterministic creation of universal cluster states with probabilistic Bell measurements and 3-qubit resource states

We develop a scheme for generating a universal qubit cluster state using probabilistic Bell measurements without the need for feed-forward or long-time quantum memories. Borrowing ideas from percolation theory we numerically show that using unambiguous Bell measurements that succeed with 75% success probability, one could build a cluster state with an underlying pyrochlore geometry such that the probability of having a spanning cluster in a chosen direction approaches unity in the limit of an infinite lattice size. The initial resources required for the generation of a universal state in our protocol are 3-qubit cluster states that are within experimental reach and are a minimal resource for a Bell-measurement-based percolation proposal. Since single and multi-photon losses can be detected in Bell measurements, our protocol raises the prospect of a fully error-robust scheme.

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arXiv2014

Quantum correlations of two-qubit states with one maximally mixed marginal

We investigate the entanglement, CHSH nonlocality, fully entangled fraction and symmetric extendibility of two-qubit states that have a single maximally mixed marginal. Within this set of states, the steering ellipsoid formalism has recently highlighted an interesting family of so-called 'maximally obese' states. These are found to have extremal quantum correlation properties that are significant in the steering ellipsoid picture and for the study of two-qubit states in general.

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arXiv2014

Quantum Steering Ellipsoids

The quantum steering ellipsoid of a two-qubit state is the set of Bloch vectors that Bob can collapse Alice's qubit to, considering all possible measurements on his qubit. We provide an elementary construction of the ellipsoid for arbitrary states, calculate its volume, and explain how this geometric representation can be made faithful. The representation provides a range of new results, and uncovers new features, such as the existence of "incomplete steering" in separable states. We show that entanglement can be analysed in terms of three geometric features of the ellipsoid, and prove that a state is separable if and only if it obeys a "nested tetrahedron" condition.

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arXiv2014

Operational constraints on state-dependent formulations of quantum error-disturbance trade-off relations

We argue for an operational requirement that all state-dependent measures of disturbance should satisfy. Motivated by this natural criterion, we prove that in any $d$-dimensional Hilbert space and for any pair of non-commuting operators, $A$ and $B$, there exists a set of at least $2^{d-1}$ zero-noise, zero-disturbance (ZNZD) states, for which the first observable can be measured without noise and the second will not be disturbed. Moreover, we show that it is possible to construct such ZNZD states for which the expectation value of the commutator $[A,B]$ does not vanish. Therefore any state-dependent error-disturbance relation, based on the expectation value of the commutator as a lower bound, must violate the operational requirement. We also discuss Ozawa's state-dependent error-disturbance relation in light of our results and show that the disturbance measure used in this relation exhibits unphysical properties. We conclude that the trade-off is inevitable only between state-independent measures of error and disturbance.

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arXiv2014

Quantum and classical entropic uncertainty relations

How much of the uncertainty in predicting measurement outcomes for non-commuting quantum observables is genuinely quantum mechanical? We provide a natural decomposition of the total entropic uncertainty of two non-commuting observables into a classical component, and an intrinsically quantum mechanical component. We show that the total quantum component in a state is never lower or upper bounded by any state-independent quantities, but instead admits "purity-based" lower bounds that generalize entropic formulations such as the Maassen-Uffink relation. These relations reveal a non-trivial interplay between quantum and classical randomness in any finite-dimensional state.

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arXiv2013

On the experimental verification of quantum complexity in linear optics

The first quantum technologies to solve computational problems that are beyond the capabilities of classical computers are likely to be devices that exploit characteristics inherent to a particular physical system, to tackle a bespoke problem suited to those characteristics. Evidence implies that the detection of ensembles of photons, which have propagated through a linear optical circuit, is equivalent to sampling from a probability distribution that is intractable to classical simulation. However, it is probable that the complexity of this type of sampling problem means that its solution is classically unverifiable within a feasible number of trials, and the task of establishing correct operation becomes one of gathering sufficiently convincing circumstantial evidence. Here, we develop scalable methods to experimentally establish correct operation for this class of sampling algorithm, which we implement with two different types of optical circuits for 3, 4, and 5 photons, on Hilbert spaces of up to 50,000 dimensions. With only a small number of trials, we establish a confidence >99% that we are not sampling from a uniform distribution or a classical distribution, and we demonstrate a unitary specific witness that functions robustly for small amounts of data. Like the algorithmic operations they endorse, our methods exploit the characteristics native to the quantum system in question. Here we observe and make an application of a "bosonic clouding" phenomenon, interesting in its own right, where photons are found in local groups of modes superposed across two locations. Our broad approach is likely to be practical for all architectures for quantum technologies where formal verification methods for quantum algorithms are either intractable or unknown.

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arXiv2013

Loss Tolerance with a Concatenated Graph State

A new way of addressing loss errors is introduced which combines ideas from measurement-based quantum computation and concatenated quantum codes, allowing for universal quantum computation. It is shown that for the case where leakage is detected upon measurement, the scheme performs well under 23% loss rate. For loss rates below 10%, this approach performs better than the best scheme known up to date [Phys. Rev.Lett., 97(12):120501]. If lost qubits are tagged prior to measurement, it can tolerate up to 50% loss. The overhead per logical qubit is shown to be significantly lower than other schemes. The obtention of the threshold is entirely analytic.

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arXiv2013

Noise effects and tomography of remote entangled spins in quantum dots

We investigate how decoherence affects the entanglement established between two quantum dots in micro cavities, and propose a tomographic scheme able to measure the entangled state. The scheme we consider establishes the entanglement via the exchange and measurement of a photon. Making the realistic assumption of noise dominated by pure-dephasing processes, we find that the photon must be exchanged and measured on timescales shorter than the quantum dots' characteristic dephasing time for appreciable levels of entanglement to be achieved. The tomographic scheme is able to reconstruct the full density matrix of the quantum dots, and requires only single spin rotations and the injection of an additional photon. Remarkably, we find that the additional photon need not be exchanged and measured on a timescale shorter than the dephasing time for accurate tomography, and also allows many to be used in order to increase the measurement signal.

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arXiv2012

Distinct Quantum States Can Be Compatible with a Single State of Reality

Perhaps the quantum state represents information about reality, and not reality directly. Wave function collapse is then possibly no more mysterious than a Bayesian update of a probability distribution given new data. We consider models for quantum systems with measurement outcomes determined by an underlying physical state of the system but where several quantum states are consistent with a single underlying state---i.e., probability distributions for distinct quantum states overlap. Significantly, we demonstrate by example that additional assumptions are always necessary to rule out such a model.

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arXiv2012

On the reality of the quantum state

Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds directly to reality. However, there is a long history of suggestions that a quantum state (even a pure state) represents only knowledge or information about some aspect of reality. Here we show that any model in which a quantum state represents mere information about an underlying physical state of the system, and in which systems that are prepared independently have independent physical states, must make predictions which contradict those of quantum theory.

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arXiv2012

Can different quantum state vectors correspond to the same physical state? An experimental test

A century on from the development of quantum theory, the interpretation of a quantum state is still discussed. If a physicist claims to have produced a system with a particular wave function, does this represent directly a physical wave of some kind, or is the wave function merely a summary of knowledge, or information, about the system? A recent no-go theorem shows that models in which the wave function is not physical, but corresponds only to an experimenter's information about a hypothetical real state of the system, must make different predictions from quantum theory when a certain test is carried out. Here we report on an experimental implementation using trapped ions. Within experimental error, the results confirm quantum theory. We analyse which kinds of theories are ruled out.

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arXiv2012

Quantum lost property: a possible operational meaning for the Hilbert-Schmidt product

Minimum error state discrimination between two mixed states ρand σcan be aided by the receipt of "classical side information" specifying which states from some convex decompositions of ρand σapply in each run. We quantify this phenomena by the average trace distance, and give lower and upper bounds on this quantity as functions of ρand σ. The lower bound is simply the trace distance between ρand σ, trivially seen to be tight. The upper bound is \sqrt{1 - tr(ρσ)}, and we conjecture that this is also tight. We reformulate this conjecture in terms of the existence of a pair of "unbiased decompositions", which may be of independent interest, and prove it for a few special cases. Finally, we point towards a link with a notion of non-classicality known as preparation contextuality.

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arXiv2012

The WAY theorem and the quantum resource theory of asymmetry

The WAY theorem establishes an important constraint that conservation laws impose on quantum mechanical measurements. We formulate the WAY theorem in the broader context of resource theories, where one is constrained to a subset of quantum mechanical operations described by a symmetry group. Establishing connections with the theory of quantum state discrimination we obtain optimal unitaries describing the measurement of arbitrary observables, explain how prior information can permit perfect measurements that circumvent the WAY constraint, and provide a framework that establishes a natural ordering on measurement apparatuses through a decomposition into asymmetry and charge subsystems.

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arXiv2012

Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction

How would the world appear to us if its ontology was that of classical mechanics but every agent faced a restriction on how much they could come to know about the classical state? We show that in most respects, it would appear to us as quantum. The statistical theory of classical mechanics, which specifies how probability distributions over phase space evolve under Hamiltonian evolution and under measurements, is typically called Liouville mechanics, so the theory we explore here is Liouville mechanics with an epistemic restriction. The particular epistemic restriction we posit as our foundational postulate specifies two constraints. The first constraint is a classical analogue of Heisenberg's uncertainty principle -- the second-order moments of position and momentum defined by the phase-space distribution that characterizes an agent's knowledge are required to satisfy the same constraints as are satisfied by the moments of position and momentum observables for a quantum state. The second constraint is that the distribution should have maximal entropy for the given moments. Starting from this postulate, we derive the allowed preparations, measurements and transformations and demonstrate that they are isomorphic to those allowed in Gaussian quantum mechanics and generate the same experimental statistics. We argue that this reconstruction of Gaussian quantum mechanics constitutes additional evidence in favour of a research program wherein quantum states are interpreted as states of incomplete knowledge, and that the phenomena that do not arise in Gaussian quantum mechanics provide the best clues for how one might reconstruct the full quantum theory.

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arXiv2012

How Einstein and/or Schroedinger should have discovered Bell's theorem in 1936

This note shows how one can be led from considerations of quantum steering to Bell's theorem. The point is that steering remote systems by choosing between two measurements can be described in a local theory if we take quantum states to be associated many-to-one with the underlying "real states" of the world. Once one adds a third measurement this is no longer possible. Historically this is not how Bell's theorem arose - there are slight and subtle differences in the arguments - but it could have been.

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arXiv2012

Quantum Mutual Information Along Unitary Orbits

Motivated by thermodynamic considerations, we analyse the variation of the quantum mutual information on a unitary orbit of a bipartite system's state, with and without global constraints such as energy conservation. We solve the full optimisation problem for the smallest system of two qubits, and explore thoroughly the effect of unitary operations on the space of reduced-state spectra. We then provide applications of these ideas to physical processes within closed quantum systems, such as a generalized collision model approach to thermal equilibrium and a global Maxwell demon playing tricks on local observers. For higher dimensions, the maximization of correlations is relatively straightforward for equal-sized subsystems, however their minimisation displays non-trivial structures. We characterise a set of separable states in which the minimally correlated state resides: a collection of classically correlated states admitting a particular "Young tableau" form. Furthermore, a partial order exists on this set with respect to individual marginal entropies, and the presence of a "see-saw effect" for these entropies forces a finer analysis to determine the optimal tableau.

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arXiv2012

Maximally and minimally correlated states attainable within a closed evolving system

The amount of correlation attainable between the components of a quantum system is constrained if the system is closed. We provide some examples, largely from the field of quantum thermodynamics, where knowing the maximal possible variation in correlations is useful. The optimization problem it raises requires us to search for the maximally and minimally correlated states on a unitary orbit, with and without energy conservation. This is fully solvable for the smallest system of two qubits. For larger systems the problem is reduced to a manageable, classical optimization.

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arXiv2012

Efficient entanglement length measurements for photonic cluster state sources

We present a procedure for confirming the generation of long strings of photons in an entangled (cluster) state that does not rely on complete state tomography and that works even at low collection efficiencies. The scheme has the added advantage of being passive - it does not require switching of optical elements to perform measurements in different bases for instance.

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