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Valerio Scarani

Publications and source records attributed to Valerio Scarani.

At least 109 records · Page 6Linked to original sources
arXiv2016

Device-independent parallel self-testing of two singlets

Device-independent self-testing is the possibility of certifying the quantum state and the measurements, up to local isometries, using only the statistics observed by querying uncharacterized local devices. In this paper, we study parallel self-testing of two maximally entangled pairs of qubits: in particular, the local tensor product structure is not assumed but derived. We prove two criteria that achieve the desired result: a double use of the Clauser-Horne-Shimony-Holt inequality and the $3\times 3$ Magic Square game. This demonstrate that the magic square game can only be perfectly won by measureing a two-singlets state. The tolerance to noise is well within reach of state-of-the-art experiments.

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arXiv2015

State complexity and quantum computation

The complexity of a quantum state may be closely related to the usefulness of the state for quantum computation. We discuss this link using the tree size of a multiqubit state, a complexity measure that has two noticeable (and, so far, unique) features: it is in principle computable, and non-trivial lower bounds can be obtained, hence identifying truly complex states. In this paper, we first review the definition of tree size, together with known results on the most complex three and four qubits states. Moving to the multiqubit case, we revisit a mathematical theorem for proving a lower bound on tree size that scales superpolynomially in the number of qubits. Next, states with superpolynomial tree size, the Immanant states, the Deutsch-Jozsa states, the Shor's states and the subgroup states, are described. We show that the universal resource state for measurement based quantum computation, the 2D-cluster state, has superpolynomial tree size. Moreover, we show how the complexity of subgroup states and the 2D cluster state can be verified efficiently. The question of how tree size is related to the speed up achieved in quantum computation is also addressed. We show that superpolynomial tree size of the resource state is essential for measurement based quantum computation. The necessary role of large tree size in the circuit model of quantum computation is still a conjecture; and we prove a weaker version of the conjecture.

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arXiv2015

The device-independent outlook on quantum physics (lecture notes on the power of Bell's theorem)

This text is an introduction to an operational outlook on Bell inequalities, which has been very fruitful in the past few years. It has lead to the recognition that Bell tests have their own place in applied quantum technologies, because they quantify non-classicality in a device-independent way, that is, without any need to describe the degrees of freedom under study and the measurements that are performed. At the more fundamental level, the same device-independent outlook has allowed the falsification of several other alternative models that could hope to reproduce the observed statistics while keeping some classical features that quantum theory denies; and it has shed new light on the long-standing quest for deriving quantum theory from physical principles.

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arXiv2015

Limiting the complexity of quantum states: a toy theory

This paper discusses a restriction of quantum theory, in which very complex states would be excluded. The toy theory is phrased in the language of the circuit model for quantum computing, its key ingredient being a limitation on the number of interactions that \textit{each} qubit may undergo. As long as one stays in the circuit model, the toy theory is consistent and may even match what we shall be ever able to do in a controlled laboratory experiment. The direct extension of the restriction beyond the circuit model conflicts with observed facts: the possibility of restricting the complexity of quantum state, while saving phenomena, remains an open question.

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arXiv2015

Physical characterization of quantum devices from nonlocal correlations

In the device-independent approach to quantum information theory, quantum systems are regarded as black boxes which, given an input (the measurement setting), return an output (the measurement result). These boxes are then treated regardless of their actual internal working. In this paper, we develop SWAP, a theoretical concept which, in combination with the tool of semi-definite methods for the characterization of quantum correlations, allows us to estimate physical properties of the black boxes from the observed measurement statistics. We find that the SWAP tool provides bounds orders of magnitude better than previously-known techniques (e.g.: for a CHSH violation larger than 2.57, SWAP predicts a singlet fidelity greater than 70%). This method also allows us to deal with hitherto intractable cases such as robust device-independent self-testing of non-maximally entangled two-qutrit states in the CGLMP scenario (for which Jordan's Lemma does not apply) and the device-independent certification of entangled measurements. We further apply the SWAP method to relate nonlocal correlations to work extraction and quantum dimensionality, hence demonstrating that this tool can be used to study a wide variety of properties relying on the sole knowledge of accessible statistics.

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arXiv2014

More randomness from noisy sources

Bell experiments can be used to generate private random numbers. An ideal Bell experiment would involve measuring a state of two maximally entangled qubits, but in practice any state produced is subject to noise. Here we consider how the techniques presented in arXiv:1309.3894 and arXiv:1309.3930, i.e. using an optimized Bell inequality, and taking advantage of the fact that the device provider is not our adversary, can be used to improve the rate of randomness generation in Bell-like tests performed on singlet states subject to either white or dephasing noise.

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arXiv2014

Proposal for Monitoring and Heralding Position States of Atoms in a One-Dimensional Waveguide

We study the single-photon transport in a single-mode waveguide, in which two-level atoms in spatial superpositions are embedded. We find that the transmission of the photon can be used as a non-destructive probe for coherence of the superposition. The protocol proposed is shown to be independent of the distance between the wells in which the atoms are trapped. Furthermore, we show that by looking at the transmission in a suitable regime, a maximally entangled state can be post-selected from an unknown superposition.

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arXiv2014

Excitation of two atoms by a propagating single photon pulse

We describe the interaction of two two-level atoms in free space with propagating modes of the quantized electromagnetic field, using the time-dependent Heisenberg-Langevin method. For single- photon pulses, we consider the effect of the pulse's spatial and temporal profiles on the atomic excitation. In particular, we find the ideal shape for a pulse to put exactly one excitation in any desired state of the bi-atomic system. Furthermore, we analyze the differences in the atomic dynamics between the cases of Fock state pulses and coherent state pulses.

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arXiv2014

Quantum randomness extraction for various levels of characterization of the devices

The amount of intrinsic randomness that can be extracted from measurement on quantum systems depends on several factors: notably, the power given to the adversary and the level of characterization of the devices of the authorized partners. After presenting a systematic introduction to these notions, in this paper we work in the class of least adversarial power, which is relevant for assessing setups operated by trusted experimentalists, and compare three levels of characterization of the devices. Many recent studies have focused on the so-called "device-independent" level, in which a lower bound on the amount of intrinsic randomness can be certified without any characterization. The other extreme is the case when all the devices are fully characterized: this "tomographic" level has been known for a long time. We present for this case a systematic and efficient approach to quantifying the amount of intrinsic randomness, and show that setups involving ancillas (POVMs, pointer measurements) may not be interesting here, insofar as one may extract randomness from the ancilla rather than from the system under study. Finally, we study how much randomness can be obtained in presence of an intermediate level of characterization related to the task of "steering", in which Bob's device is fully characterized while Alice's is a black box. We obtain our results here by adapting the NPA hierarchy of semidefinite programs to the steering scenario.

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arXiv2014

Robust self testing of the 3-qubit $W$ state

Self-testing is a device independent method which can be used to determine the nature of a physical system or device, without knowing any detail of the inner mechanism or the physical dimension of Hilbert space of the system. The only information required are the number of measurements, number of outputs of each measurement and the statistics of each measurement. Earlier works on self testing restricted either to two parties scenario or multipartite graph states. Here, we construct a method to self-test the three-qubit $W$ state, and show how to extend it to other pure three-qubit states. Our bounds are robust against the inevitable experimental errors.

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arXiv2014

Maximal tree size of few-qubit states

Tree size ($\rm{TS}$) is an interesting measure of complexity for multiqubit states: not only is it in principle computable, but one can obtain lower bounds for it. In this way, it has been possible to identify families of states whose complexity scales superpolynomially in the number of qubits. With the goal of progressing in the systematic study of the mathematical property of $\rm{TS}$, in this work we characterize the tree size of pure states for the case where the number of qubits is small, namely, 3 or 4. The study of three qubits does not hold great surprises, insofar as the structure of entanglement is rather simple; the maximal $\rm{TS}$ is found to be 8, reached for instance by the $|\rm{W}\rangle$ state. The study of four qubits yields several insights: in particular, the most economic description of a state is found not to be recursive. The maximal $\rm{TS}$ is found to be 16, reached for instance by a state called $|Ψ^{(4)}\rangle$ which was already discussed in the context of four-photon down-conversion experiments. We also find that the states with maximal tree size form a set of zero measure: a smoothed version of tree size over a neighborhood of a state ($ε-\rm{TS}$) reduces the maximal values to 6 and 14, respectively. Finally, we introduce a notion of tree size for mixed states and discuss it for a one-parameter family of states.

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arXiv2014

Robust and versatile black-box certification of quantum devices

Self-testing refers to the fact that, in some quantum devices, both states and measurements can be assessed in a black-box scenario, on the sole basis of the observed statistics, i.e. without reference to any prior device calibration. Only a few examples of self-testing are known, and they just provide non-trivial assessment for devices performing unrealistically close to the ideal case. We overcome these difficulties by approaching self-testing with the semi-definite programming hierarchy for the characterization of quantum correlations. This allows us to improve dramatically the robustness of previous self-testing schemes -e.g.: we show that a CHSH violation larger than 2.57 certifies a singlet fidelity of more than 70%. In addition, the versatility of the tool brings about self-testing of hitherto impossible cases, such as robust self-testing of non-maximally entangled two-qutrit states in the CGLMP scenario.

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arXiv2014

Bell nonlocality

Bell's 1964 theorem, which states that the predictions of quantum theory cannot be accounted for by any local theory, represents one of the most profound developments in the foundations of physics. In the last two decades, Bell's theorem has been a central theme of research from a variety of perspectives, mainly motivated by quantum information science, where the nonlocality of quantum theory underpins many of the advantages afforded by a quantum processing of information. The focus of this review is to a large extent oriented by these later developments. We review the main concepts and tools which have been developed to describe and study the nonlocality of quantum theory, and which have raised this topic to the status of a full sub-field of quantum information science.

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arXiv2014

More Randomness from the Same Data

Correlations that cannot be reproduced with local variables certify the generation of private randomness. Usually, the violation of a Bell inequality is used to quantify the amount of randomness produced. Here, we show how private randomness generated during a Bell test can be directly quantified from the observed correlations, without the need to process these data into an inequality. The frequency with which the different measurement settings are used during the Bell test can also be taken into account. This improved analysis turns out to be very relevant for Bell tests performed with a finite collection efficiency. In particular, applying our technique to the data of a recent experiment [Christensen et al., Phys. Rev. Lett. 111, 130406 (2013)], we show that about twice as much randomness as previously reported can be potentially extracted from this setup.

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arXiv2013

Analysis of a proposal for a realistic loophole-free Bell test with atom-light entanglement

The violation of Bell inequalities where both detection and locality loopholes are closed is crucial for device independent assessments of quantum information. While of technological nature, the simultaneous closing of both loopholes still remains a challenge. In Nat. Commun. 4:2104(2013), a realistic setup to produce an atom-photon entangled state that could reach a loophole free Bell inequality violation within current experimental technology was proposed. Here we improve the analysis of this proposal by giving an analytical treatment that shows that the state proposed in Nat. Commun. 4:2104(2013) could in principle violate a Bell inequality for arbitrarily low photodetection efficiency. Moreover, it is also able to violate a Bell inequality considering only atomic and homodyne measurements eliminating the need to consider inefficient photocounting measurements. In this case, the maximum Clauser-Horne-Shimony-Holt (CHSH) inequality violation achievable is 2.29, and the minimum transmission required for violation is about 68%. Finally, we show that by postselecting on an atomic measurement, one can engineer superpositions of coherent states for various coherent state amplitudes.

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arXiv2013

Device-independent certification of the teleportation of a qubit

We want to certify in a black box scenario that two parties simulating the teleportation of a qubit are really using quantum resources. If active compensation is part of the simulation, perfect teleportation can be faked with purely classical means. If active compensation is not implemented, a classical simulation is necessarily imperfect: in this case, we provide bounds for certification of quantumness using only the observed statistics. The usual figure of merit, namely the average fidelity of teleportation, turns out to be too much of a coarse-graining of the available statistical information in the case of a black-box assessment.

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arXiv2013

Tree-size complexity of multiqubit states

Complexity is often invoked alongside size and mass as a characteristic of macroscopic quantum objects. In 2004, Aaronson introduced the \textit{tree size} (TS) as a computable measure of complexity and studied its basic properties. In this paper, we improve and expand on those initial results. In particular, we give explicit characterizations of a family of states with superpolynomial complexity $n^{Ω(\log n)}= \mathrm{TS} =O(\sqrt{n}!)$ in the number of qubits $n$; and we show that any matrix-product state whose tensors are of dimension $D\times D$ has polynomial complexity $\mathrm{TS}=O(n^{\log_2 2D})$.

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