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Frédéric Grosshans

Publications and source records attributed to Frédéric Grosshans.

At least 37 records · Page 2Linked to original sources
arXiv2020

Breaking simple quantum position verification protocols with little entanglement

Instantaneous nonlocal quantum computation (INQC) evades apparent quantum and relativistic constraints and allows to attack generic quantum position verification (QPV) protocols (aiming at securely certifying the location of a distant prover) at an exponential entanglement cost. We consider adversaries sharing maximally entangled pairs of qudits and find low-dimensional INQC attacks against the simple practical family of QPV protocols based on single photons polarized at an angle $θ$. We find exact attacks against some rational angles, including some sitting outside of the Clifford hierarchy (e.g. $π/6$), and show no $θ$ allows to tolerate errors higher than $\simeq 5\cdot 10^{-3}$ against adversaries holding two ebits per protocol's qubit.

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arXiv2020

Building trust for continuous variable quantum states

In this work we develop new methods for the characterisation of continuous variable quantum states using heterodyne measurement in both the trusted and untrusted settings. First, building on quantum state tomography with heterodyne detection, we introduce a reliable method for continuous variable quantum state certification, which directly yields the elements of the density matrix of the state considered with analytical confidence intervals. This method neither needs mathematical reconstruction of the data nor discrete binning of the sample space, and uses a single Gaussian measurement setting. Second, beyond quantum state tomography and without its identical copies assumption, we promote our reliable tomography method to a general efficient protocol for verifying continuous variable pure quantum states with Gaussian measurements against fully malicious adversaries, i.e., making no assumptions whatsoever on the state generated by the adversary. These results are obtained using a new analytical estimator for the expected value of any operator acting on a continuous variable quantum state with bounded support over the Fock basis, computed with samples from heterodyne detection of the state.

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arXiv2020

Stellar representation of non-Gaussian quantum states

The so-called stellar formalism allows to represent the non-Gaussian properties of single-mode quantum states by the distribution of the zeros of their Husimi Q-function in phase-space. We use this representation in order to derive an infinite hierarchy of single-mode states based on the number of zeros of the Husimi Q-function, the stellar hierarchy. We give an operational characterisation of the states in this hierarchy with the minimal number of single-photon additions needed to engineer them, and derive equivalence classes under Gaussian unitary operations. We study in detail the topological properties of this hierarchy with respect to the trace norm, and discuss implications for non-Gaussian state engineering and continuous variable quantum computing.

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arXiv2019

Distributing Graph States Over Arbitrary Quantum Networks

Multipartite entangled states are great resources for quantum networks. In this work we study the distribution, or routing, of entangled states over fixed, but arbitrary, physical networks. Our simplified model represents each use of a quantum channel as the sharing of a Bell pair; local operations and classical communications are considered to be free. We introduce two protocols to distribute respectively Greenberger-Horne-Zeilinger (GHZ) states and arbitrary graph states over arbitrary quantum networks. The GHZ states distribution protocol takes a single step and is optimal in terms of the number of Bell pairs used; the graph state distribution protocol uses at most twice as many Bell pairs and steps than the optimal routing protocol for the worst case scenario.

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arXiv2019

Random coding for sharing bosonic quantum secrets

We consider a protocol for sharing quantum states using continuous variable systems. Specifically we introduce an encoding procedure where bosonic modes in arbitrary secret states are mixed with several ancillary squeezed modes through a passive interferometer. We derive simple conditions on the interferometer for this encoding to define a secret sharing protocol and we prove that they are satisfied by almost any interferometer. This implies that, if the interferometer is chosen uniformly at random, the probability that it may not be used to implement a quantum secret sharing protocol is zero. Furthermore, we show that the decoding operation can be obtained and implemented efficiently with a Gaussian unitary using a number of single-mode squeezers that is at most twice the number of modes of the secret, regardless of the number of players. We benchmark the quality of the reconstructed state by computing the fidelity with the secret state as a function of the input squeezing.

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arXiv2019

Semi-device-independent quantum money with coherent states

The no-cloning property of quantum mechanics allows unforgeability of quantum banknotes and credit cards. Quantum credit card protocols involve a bank, a client and a payment terminal, and their practical implementation typically relies on encoding information on weak coherent states of light. Here, we provide a security proof in this practical setting for semi-device-independent quantum money with classical verification, involving an honest bank, a dishonest client and a potentially untrusted terminal. Our analysis uses semidefinite programming in the coherent state framework and aims at simultaneously optimizing over the noise and losses introduced by a dishonest party. We discuss secure regimes of operation in both fixed and randomized phase settings, taking into account experimental imperfections. Finally, we study the evolution of protocol security in the presence of a decohering optical quantum memory and identify secure credit card lifetimes for a specific configuration.

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arXiv2018

Investigating the optimality of ancilla-assisted linear optical Bell measurements

In the last decade Grice and Ewert and van Loock found linear optical networks achieving near-unit efficiency unambiguous Bell state discrimination, when fed with increasingly complex ancillary states. However, except for the vacuum ancilla case, the optimality of these schemes is unknown. Here, the optimality of these networks is investigated through analytical and numerical means. We show an analytical upper bound to the success probability for interferometers that preserve the polarization of the input photons, saturated by both Grice's and Evert-van Loock's strategies. Furthermore, such an upper bound links the complexity of their ancilla states with the scaling of their performance. We also show a computer-aided approach to the optimization of such measurement schemes for generic interferometers, by simulating an optical network supplied with various kinds of ancillary input states. We numerically confirms the optimality of known small schemes. We use both methods to investigate other ancilla states, some of them never studied before.

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arXiv2017

Factoring Safe Semiprimes with a Single Quantum Query

Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform efficiently. SFA thus consists of a \emph{quantum order finding algorithm} (QOFA), bookended by classical routines which, given the order, return the factors. But, with probability up to $1/2$, these classical routines fail, and QOFA must be rerun. We modify these routines using elementary results in number theory, improving the likelihood that they return the factors. The resulting quantum factoring algorithm is better than SFA at factoring safe semiprimes, an important class of numbers used in cryptography. With just one call to QOFA, our algorithm almost always factors safe semiprimes. As well as a speed-up, improving efficiency gives our algorithm other, practical advantages: unlike SFA, it does not need a randomly picked input, making it simpler to construct in the lab; and in the (unlikely) case of failure, the same circuit can be rerun, without modification. We consider generalizing this result to other cases, although we do not find a simple extension, and conclude that SFA is still the best algorithm for general numbers (non safe semiprimes, in other words). Even so, we present some simple number theoretic tricks for improving SFA in this case.

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arXiv2016

Thermalization in a 1D Rydberg gas: validity of the microcanonical ensemble hypothesis

We question the microcanonical hypothesis, often made to account for the thermalization of complex closed quantum systems, on the specific example of a chain of two-level atoms optically driven by a resonant laser beam and strongly interacting via Rydberg-Rydberg dipole-dipole interactions. Along its (necessarily unitary) evolution, this system is indeed expected to thermalize, i.e. observables, such as the number of excitations, stop oscillating and reach equilibrium-like expectation values. The latter are often calculated through assuming the system can be effectively described by a thermal-like microcanonical state. Here, we compare the distribution of excitations in the chain calculated either according to the microcanonical assumption or through direct exact numerical simulation. This allows us to show the limitations of the thermal equilibrium hypothesis and precise its applicability conditions.

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arXiv2016

Unidimensional continuous-variable quantum key distribution

We propose the continuous-variable quantum key distribution protocol based on the Gaussian modulation of a single quadrature of the coherent states of light, which is aimed to provide simplified implementation compared to the symmetrically modulated Gaussian coherent-state protocols. The protocol waives the necessity in phase quadrature modulation and the corresponding channel transmittance estimation. The security of the protocol against collective attacks in a generally phase-sensitive Gaussian channels is analyzed and is shown achievable upon certain conditions. Robustness of the protocol to channel imperfections is compared to that of the symmetrical coherent-state protocol. The simplified unidimensional protocol is shown possible at a reasonable quantitative cost in terms of key rate and of tolerable channel excess noise.

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arXiv2015

A Tight Lower Bound for the BB84-states Quantum-Position-Verification Protocol

We use the entanglement sampling techniques developed by Dupuis, Fawzi and Wehner to find a lower bound on the entanglement needed by a coalition of cheater attacking the quantum position verification protocol using the four BB84 states in the scenario where the cheaters have no access to a quantum channel but share a (possibly mixed) entangled state $\tildeΦ$. For a protocol using n qubits, a necessary condition for cheating is that the max- relative entropy of entanglement $E_{\max}(\tildeΦ)\ge n-O(\log n)$. This improves previously known best lower bound by a factor $\sim4$, and it is essentially tight, since this protocol is vulnerable to a teleportation based attack using $n-O(1)$ ebits of entanglement.

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arXiv2013

Photon-Number-Splitting-attack resistant Quantum Key Distribution Protocols without sifting

We propose a family of sifting-less quantum-key-distribution protocols which use reverse-reconciliation, and are based on weak coherent pulses (WCPs) polarized along m different directions. When m=4, the physical part of the protocol is identical to most experimental implementations of BB84 and SARG04 protocols and they differ only in classical communications and data processing. We compute their total keyrate as function of the channel transmission T, using general information theoretical arguments and we show that they have a higher keyrate than the more standard protocols, both for fixed and optimized average photon number of the WCPs. When no decoy-state protocols (DSPs) are applied, the scaling of the keyrate with transmission is improved from T 2 for BB84 to T^(1+1/(m-2)). If a DSP is applied, we show how the keyrates scale linearly with T, with an improvement of the prefactor by 75.96 % for m=4. High values of $ m $ allow to asymptotically approach the keyrate obtained with ideal single photon pulses. The fact that the keyrates of these sifting-less protocols are higher compared to those of the aforementioned more standard protocols show that the latter are not optimal, since they do not extract all the available secret key from the experimental correlations.

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arXiv2010

Finite-size analysis of continuous-variable quantum key distribution

The goal of this paper is to extend the framework of finite size analysis recently developed for quantum key distribution to continuous-variable protocols. We do not solve this problem completely here, and we mainly consider the finite size effects on the parameter estimation procedure. Despite the fact that some questions are left open, we are able to give an estimation of the secret key rate for protocols which do not contain a postselection procedure. As expected, these results are significantly more pessimistic than the ones obtained in the asymptotic regime. However, we show that recent continuous-variable protocols are able to provide fully secure secret keys in the finite size scenario, over distances larger than 50 km.

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arXiv2009

Robust and Efficient Sifting-Less Quantum Key Distribution Protocols

We show that replacing the usual sifting step of the standard quantum-key-distribution protocol BB84 by a one-way reverse reconciliation procedure increases its robustness against photon-number-splitting (PNS) attacks to the level of the SARG04 protocol while keeping the raw key-rate of BB84. This protocol, which uses the same state and detection than BB84, is the m=4 member of a protocol-family using m polarization states which we introduce here. We show that the robustness of these protocols against PNS attacks increases exponentially with m, and that the effective keyrate of optimized weak coherent pulses decreases with the transmission T like T^{1+1/(m-2)}.

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arXiv2008

Delayed-choice test of complementarity with single photons

We report an experimental test of complementarity using clock-triggered single-photon pulses emitted by an individual N-V color center in a diamond nanocrystal. The single photons are sent into a Mach-Zehnder interferometer with an output beamsplitter of adjustable reflection coefficient R. In addition, the choice of introducing or removing this beamsplitter is random and relativistically space-like separated from the entering of the photon inside the interferometer, as required for the Wheeler's delayed-choice regime. Each set value of R allows us to observe interference with visibility V and to obtain incomplete which-path information characterized by the distinguishability D. The measured values of V and D are found to obey the complementarity relation V^2 + D^2 =< 1.

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arXiv2007

Enhancing single-molecule photostability by optical feedback from quantum-jump detection

We report an optical technique that yields an enhancement of single-molecule photostability, by greatly suppressing photobleaching pathways which involve photoexcitation from the triplet state. This is accomplished by dynamically switching off the excitation laser when a quantum-jump of the molecule to the triplet state is optically detected. This procedure leads to a lengthened single-molecule observation time and an increased total number of detected photons. The resulting improvement in photostability unambiguously confirms the importance of photoexcitation from the triplet state in photobleaching dynamics, and may allow the investigation of new phenomena at the single-molecule level.

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arXiv2006

Experimental realization of Wheeler's delayed-choice GedankenExperiment

The quantum "mystery which cannot go away" (in Feynman's words) of wave-particle duality is illustrated in a striking way by Wheeler's delayed-choice GedankenExperiment. In this experiment, the configuration of a two-path interferometer is chosen after a single-photon pulse has entered it : either the interferometer is \textit{closed} (\textit{i.e.} the two paths are recombined) and the interference is observed, or the interferometer remains \textit{open} and the path followed by the photon is measured. We report an almost ideal realization of that GedankenExperiment, where the light pulses are true single photons, allowing unambiguous which-way measurements, and the interferometer, which has two spatially separated paths, produces high visibility interference. The choice between measuring either the 'open' or 'closed' configuration is made by a quantum random number generator, and is space-like separated -- in the relativistic sense -- from the entering of the photon into the interferometer. Measurements in the closed configuration show interference with a visibility of 94%, while measurements in the open configuration allow us to determine the followed path with an error probability lower than 1%.

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