arXiv subjects

Ludovico Lami

Publications and source records attributed to Ludovico Lami.

At least 73 records · Page 4Linked to original sources

arXiv2023

On tests of the quantum nature of gravitational interactions in presence of non-linear corrections to quantum mechanics

When two particles interact primarily through gravity and follow the laws of quantum mechanics, the generation of entanglement is considered a hallmark of the quantum nature of the gravitational interaction. However, we demonstrate that entanglement dynamics can also occur in the presence of a weak quantum interaction and non-linear corrections to local quantum mechanics, even if the gravitational interaction is classical or absent at short distances. This highlights the importance of going beyond entanglement detection to conclusively test the quantum character of gravity, and it requires a thorough examination of the strength of other quantum forces and potential non-linear corrections to quantum mechanics in the realm of large masses.

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arXiv2023

Fundamental limitations to key distillation from Gaussian states with Gaussian operations

We establish fundamental upper bounds on the amount of secret key that can be extracted from quantum Gaussian states by using only local Gaussian operations, local classical processing, and public communication. For one-way public communication, or when two-way public communication is allowed but Alice and Bob first perform destructive local Gaussian measurements, we prove that the key is bounded by the Rényi-$2$ Gaussian entanglement of formation $E_{F,2}^{\mathrm{\scriptscriptstyle G}}$. Since the inequality is saturated for pure Gaussian states, this yields an operational interpretation of the Rényi-$2$ entropy of entanglement as the secret key rate of pure Gaussian states that is accessible with Gaussian operations and one-way communication. In the general setting of two-way communication and arbitrary interactive protocols, we argue that $2 E_{F,2}^{\mathrm{\scriptscriptstyle G}}$ is still an upper bound on the extractable key. We conjecture that the factor of $2$ is spurious, which would imply that $E_{F,2}^{\mathrm{\scriptscriptstyle G}}$ coincides with the secret key rate of Gaussian states under Gaussian measurements and two-way public communication. We use these results to prove a gap between the secret key rates obtainable with arbitrary versus Gaussian operations. Such a gap is observed for states produced by sending one half of a two-mode squeezed vacuum through a pure loss channel, in the regime of sufficiently low squeezing or sufficiently high transmissivity. Finally, for a wide class of Gaussian states that includes all two-mode states, we prove a recently proposed conjecture on the equality between $E_{F,2}^{\mathrm{\scriptscriptstyle G}}$ and the Gaussian intrinsic entanglement. The unified entanglement quantifier emerging from such an equality is then endowed with a direct operational interpretation as the value of a quantum teleportation game.

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arXiv2023

Postselected quantum hypothesis testing

We study a variant of quantum hypothesis testing wherein an additional 'inconclusive' measurement outcome is added, allowing one to abstain from attempting to discriminate the hypotheses. The error probabilities are then conditioned on a successful attempt, with inconclusive trials disregarded. We completely characterise this task in both the single-shot and asymptotic regimes, providing exact formulas for the optimal error probabilities. In particular, we prove that the asymptotic error exponent of discriminating any two quantum states $ρ$ and $σ$ is given by the Hilbert projective metric $D_{\max}(ρ\|σ) + D_{\max}(σ\| ρ)$ in asymmetric hypothesis testing, and by the Thompson metric $\max \{ D_{\max}(ρ\|σ), D_{\max}(σ\| ρ) \}$ in symmetric hypothesis testing. This endows these two quantities with fundamental operational interpretations in quantum state discrimination. Our findings extend to composite hypothesis testing, where we show that the asymmetric error exponent with respect to any convex set of density matrices is given by a regularisation of the Hilbert projective metric. We apply our results also to quantum channels, showing that no advantage is gained by employing adaptive or even more general discrimination schemes over parallel ones, in both the asymmetric and symmetric settings. Our state discrimination results make use of no properties specific to quantum mechanics and are also valid in general probabilistic theories.

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arXiv2023

Continuity of the relative entropy of resource

A criterion of local continuity of the relative entropy of resource -- the relative entropy distance to the set of free states -- is obtained. Several basic corollaries of this criterion are presented. Applications to the relative entropy of entanglement in multipartite quantum systems are considered. It is shown, in particular, that local continuity of any relative entropy of multipartite entanglement follows from local continuity of the quantum mutual information.

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arXiv2023

Pretty good measurement for bosonic Gaussian ensembles

The pretty good measurement is a fundamental analytical tool in quantum information theory, giving a method for inferring the classical label that identifies a quantum state chosen probabilistically from an ensemble. Identifying and constructing the pretty good measurement for the class of bosonic Gaussian states is of immediate practical relevance in quantum information processing tasks. Holevo recently showed that the pretty good measurement for a bosonic Gaussian ensemble is a bosonic Gaussian measurement that attains the accessible information of the ensemble (IEEE Trans. Inf. Theory, 66(9):5634-564, 2020). In this paper, we provide an alternate proof of Gaussianity of the pretty good measurement for a Gaussian ensemble of multimode bosonic states, with a focus on establishing an explicit and efficiently computable Gaussian description of the measurement. We also compute an explicit form of the mean square error of the pretty good measurement, which is relevant when using it for parameter estimation. Generalizing the pretty good measurement is a quantum instrument, called the pretty good instrument. We prove that the post-measurement state of the pretty good instrument is a faithful Gaussian state if the input state is a faithful Gaussian state whose covariance matrix satisfies a certain condition. Combined with our previous finding for the pretty good measurement and provided that the same condition holds, it follows that the expected output state is a faithful Gaussian state as well. In this case, we compute an explicit Gaussian description of the post-measurement and expected output states. Our findings imply that the pretty good instrument for bosonic Gaussian ensembles is no longer merely an analytical tool, but that it can also be implemented experimentally in quantum optics laboratories.

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arXiv2023

Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme

The relative entropy of entanglement $E_R$ is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any state admits a closest separable state, even in infinite dimensions; also, $E_R$ is everywhere lower semi-continuous. We use this to derive a dual variational expression for $E_R$ in terms of an external supremum instead of infimum. These results, which seem to have gone unnoticed so far, hold not only for the relative entropy of entanglement and its multi-partite generalisations, but also for many other similar resource quantifiers, such as the relative entropy of non-Gaussianity, of non-classicality, of Wigner negativity $\unicode{8212}$ more generally, all relative entropy distances from the sets of states with non-negative $λ$-quasi-probability distribution. The crucial hypothesis underpinning all these applications is the weak*-closedness of the cone generated by free states, and for this reason the techniques we develop involve a bouquet of classical results from functional analysis. We complement our analysis by giving explicit and asymptotically tight continuity estimates for $E_R$ and closely related quantities in the presence of an energy constraint.

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arXiv2023

Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols

The quantum relative entropy is known to play a key role in determining the asymptotic convertibility of quantum states in general resource-theoretic settings, often constituting the unique monotone that is relevant in the asymptotic regime. We show that this is no longer the case when one allows stochastic protocols that may only succeed with some probability, in which case the quantum relative entropy is insufficient to characterize the rates of asymptotic state transformations, and a new entropic quantity based on a regularization of the Hilbert projective metric comes into play. Such a scenario is motivated by a setting where the cost associated with transformations of quantum states, typically taken to be the number of copies of a given state, is instead identified with the size of the quantum memory needed to realize the protocol. Our approach allows for constructing transformation protocols that achieve strictly higher rates than those imposed by the relative entropy. Focusing on the task of resource distillation, we give broadly applicable strong converse bounds on the asymptotic rates of probabilistic distillation protocols, and show them to be tight in relevant settings such as entanglement distillation with non-entangling operations. This generalizes and extends previously known limitations that only applied to deterministic protocols. Our methods are based on recent results for probabilistic one-shot transformations as well as a new asymptotic equipartition property for the projective relative entropy.

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arXiv2023

Classical shadow tomography for continuous variables quantum systems

In this article we develop a continuous variable (CV) shadow tomography scheme with wide ranging applications in quantum optics. Our work is motivated by the increasing experimental and technological relevance of CV systems in quantum information, quantum communication, quantum sensing, quantum simulations, quantum computing and error correction. We introduce two experimentally realisable schemes for obtaining classical shadows of CV (possibly non-Gaussian) quantum states using only randomised Gaussian unitaries and easily implementable Gaussian measurements such as homodyne and heterodyne detection. For both schemes, we show that $N=O\big(\operatorname{poly}\big(\frac{1}ε,\log\big(\frac{1}δ\big),M_n^{r+α},\log(m)\big)\big)$ samples of an unknown $m$-mode state $ρ$ suffice to learn the expected value of any $r$-local polynomial in the canonical observables of degree $α$, both with high probability $1-δ$ and accuracy $ε$, as long as the state $ρ$ has moments of order $n>α$ bounded by $M_n$. By simultaneously truncating states and operators in energy and phase space, we are able to overcome new mathematical challenges that arise due to the infinite-dimensionality of CV systems. We also provide a scheme to learn nonlinear functionals of the state, such as entropies over any small number of modes, by leveraging recent energy-constrained entropic continuity bounds. Finally, we provide numerical evidence of the efficiency of our protocols in the case of CV states of relevance in quantum information theory, including ground states of quadratic Hamiltonians of many-body systems and cat qubit states. We expect our scheme to provide good recovery in learning relevant states of 2D materials and photonic crystals.

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arXiv2023

Computable lower bounds on the entanglement cost of quantum channels

A class of lower bounds for the entanglement cost of any quantum state was recently introduced in [arXiv:2111.02438] in the form of entanglement monotones known as the tempered robustness and tempered negativity. Here we extend their definitions to point-to-point quantum channels, establishing a lower bound for the asymptotic entanglement cost of any channel, whether finite or infinite dimensional. This leads, in particular, to a bound that is computable as a semidefinite program and that can outperform previously known lower bounds, including ones based on quantum relative entropy. In the course of our proof we establish a useful link between the robustness of entanglement of quantum states and quantum channels, which requires several technical developments such as showing the lower semicontinuity of the robustness of entanglement of a channel in the weak*-operator topology on bounded linear maps between spaces of trace class operators.

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arXiv2023

No second law of entanglement manipulation after all

Many fruitful analogies have emerged between the theories of quantum entanglement and thermodynamics, motivating the pursuit of an axiomatic description of entanglement akin to the laws of thermodynamics. A long-standing open problem has been to establish a true second law of entanglement, and in particular a unique function which governs all transformations between entangled systems, mirroring the role of entropy in thermodynamics. Contrary to previous promising evidence, here we show that this is impossible, and no direct counterpart to the second law of thermodynamics can be established. This is accomplished by demonstrating the irreversibility of entanglement theory from first principles -- assuming only the most general microscopic physical constraints of entanglement manipulation, we show that entanglement theory is irreversible under all non-entangling transformations. We furthermore rule out reversibility without significant entanglement expenditure, showing that reversible entanglement transformations require the generation of macroscopically large amounts of entanglement according to certain measures. Our results not only reveal fundamental differences between quantum entanglement transformations and thermodynamic processes, but also showcase a unique property of entanglement which distinguishes it from other known quantum resources.

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arXiv2022

Upper Bounds on the Distillable Randomness of Bipartite Quantum States

The distillable randomness of a bipartite quantum state is an information-theoretic quantity equal to the largest net rate at which shared randomness can be distilled from the state by means of local operations and classical communication. This quantity has been widely used as a measure of classical correlations, and one version of it is equal to the regularized Holevo information of the ensemble that results from measuring one share of the state. However, due to the regularization, the distillable randomness is difficult to compute in general. To address this problem, we define measures of classical correlations and prove a number of their properties, most importantly that they serve as upper bounds on the distillable randomness of an arbitrary bipartite state. We then further bound these measures from above by some that are efficiently computable by means of semi-definite programming, we evaluate one of them for the example of an isotropic state, and we remark on the relation to quantities previously proposed in the literature.

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arXiv2022

Asymptotic state transformations of continuous variable resources

We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation rates in these settings. This removes the need for asymptotic continuity, which cannot be defined in the traditional sense for infinite-dimensional systems. We consider three applications, to the resource theories of (I) optical nonclassicality, (II) entanglement, and (III) quantum thermodynamics. In cases (II) and (III), the employed monotones are the (infinite-dimensional) squashed entanglement and the free energy, respectively. For case (I), we consider the measured relative entropy of nonclassicality and prove it to be lower semicontinuous and strongly superadditive. One of our main technical contributions, and a key tool to establish these results, is a handy variational expression for the measured relative entropy of nonclassicality. Our technique then yields computable upper bounds on asymptotic transformation rates, including those achievable under linear optical elements. We also prove a number of results which guarantee that the measured relative entropy of nonclassicality is bounded on any physically meaningful state and easily computable for some classes of states of interest, e.g., Fock diagonal states. We conclude by applying our findings to the problem of cat state manipulation and noisy Fock state purification.

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arXiv2022

Quantum Optical Communication in the presence of strong attenuation noise

Is quantum communication possible over an optical fibre with transmissivity $λ\leq 1/2$ ? The answer is well known to be negative if the environment with which the incoming signal interacts is initialised in a thermal state. However, in [PRL 125:110504, 2020] the quantum capacity was found to be always bounded away from zero for all $λ>0$, a phenomenon dubbed "die-hard quantum communication" (D-HQCOM), provided that the initial environment state can be chosen appropriately (depending on $λ$). Here we show an even stronger version of D-HQCOM in the context of entanglement-assisted classical communication: entanglement assistance and control of the environment enable communication with performance at least equal to that of the ideal case of absence of noise, even if $λ>0$ is arbitrarily small. These two phenomena of D-HQCOM have technological potential provided that we are able to control the environment. How can we achieve this? Our second main result answers this question. Here we provide a fully consistent protocol to activate the phenomena of D-HQCOM without directly accessing the environment state. This is done by sending over the channel "trigger signals", i.e. signals which do not encode information, prior to the actual communication, with the goal of modifying the environment in an advantageous way. This is possible thanks to the memory effects which arise when the sender feeds signals separated by a sufficiently short temporal interval. Our results may offer a concrete scheme to communicate across arbitrarily long optical fibres, without using quantum repeaters. As a by-product of our analysis, we derive a simple Kraus representation of the thermal attenuator exploiting the associated Lindblad master equation.

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arXiv2022

Restoring quantum communication efficiency over high loss optical fibres

In the absence of quantum repeaters, quantum communication proved to be nearly impossible across optical fibres longer than $\gtrsim 20\text{ km}$ due to the drop of transmissivity below the critical threshold of $1/2$. However, if the signals fed into the fibre are separated by a sufficiently short time interval, memory effects must be taken into account. In this paper we show that by properly accounting for these effects it is possible to devise schemes that enable unassisted quantum communication across arbitrarily long optical fibres at a fixed positive qubit transmission rate. We also demonstrate how to achieve entanglement-assisted communication over arbitrarily long distances at a rate of the same order of the maximum achievable in the unassisted noiseless case.

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arXiv2022

Thermometry of Gaussian quantum systems using Gaussian measurements

We study the problem of estimating the temperature of Gaussian systems with feasible measurements, namely Gaussian and photo-detection-like measurements. For Gaussian measurements, we develop a general method to identify the optimal measurement numerically, and derive the analytical solutions in some relevant cases. For a class of single-mode states that includes thermal ones, the optimal Gaussian measurement is either Heterodyne or Homodyne, depending on the temperature regime. This is in contrast to the general setting, in which a projective measurement in the eigenbasis of the Hamiltonian is optimal regardless of temperature. In the general multi-mode case, and unlike the general unrestricted scenario where joint measurements are not helpful for thermometry (nor for any parameter estimation task), it is open whether joint Gaussian measurements provide an advantage over local ones. We conjecture that they are not useful for thermal systems, supported by partial analytical and numerical evidence. We further show that Gaussian measurements become optimal in the limit of large temperatures, while on/off photo-detection-like measurements do it for when the temperature tends to zero. Our results therefore pave the way for effective thermometry of Gaussian quantum systems using experimentally realizable measurements.

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arXiv2021

Quantum data hiding with continuous variable systems

Suppose we want to benchmark a quantum device held by a remote party, e.g. by testing its ability to carry out challenging quantum measurements outside of a free set of measurements $\mathcal{M}$. A very simple way to do so is to set up a binary state discrimination task that cannot be solved efficiently by means of free measurements. If one can find pairs of orthogonal states that become arbitrarily indistinguishable under measurements in $\mathcal{M}$, in the sense that the error probability in discrimination approaches that of a random guess, one says that there is data hiding against $\mathcal{M}$. Here we investigate data hiding in the context of continuous variable quantum systems. First, we look at the case where $\mathcal{M}=\mathrm{LOCC}$, the set of measurements implementable with local operations and classical communication. While previous studies have placed upper bounds on the maximum efficiency of data hiding in terms of the local dimension and are thus not applicable to continuous variable systems, we establish more general bounds that rely solely on the local mean photon number of the states employed. Along the way, we perform a rigorous quantitative analysis of the error introduced by the non-ideal Braunstein-Kimble quantum teleportation protocol, determining how much squeezing and local detection efficiency is needed in order to teleport an arbitrary multi-mode local state of known mean energy with a prescribed accuracy. Finally, following a seminal proposal by Sabapathy and Winter, we look at data hiding against Gaussian operations assisted by feed-forward of measurement outcomes, providing the first example of a relatively simple scheme that works with a single mode only.

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arXiv2021

Maximal gap between local and global distinguishability of bipartite quantum states

We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two orthogonal quantum states of a $n_A\times n_B$ bipartite quantum system can be discriminated via local measurements with an error probability no larger than $\frac12 \left(1 - \frac{1}{c \min\{n_A, n_B\}} \right)$, where $1\leq c\leq 2\sqrt2$ is a universal constant, and our bound scales provably optimally with the local dimensions $n_A,n_B$. Mathematically, this is achieved by showing that the distinguishability norm $\|\cdot\|_{LO}$ associated with local measurements satisfies that $\|\cdot\|_1\leq 2\sqrt2 \min\{n_A,n_B\} \|\cdot\|_{LO}$, where $\|\cdot\|_1$ is the trace norm.

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arXiv2021

Entanglement and superposition are equivalent concepts in any physical theory

We prove that any two general probabilistic theories (GPTs) are entangleable, in the sense that their composite exhibits either entangled states or entangled measurements, if and only if they are both non-classical, meaning that neither of the state spaces is a simplex. This establishes the universal equivalence of the (local) superposition principle and the existence of global entanglement, valid in a fully theory-independent way. As an application of our techniques, we show that all non-classical GPTs exhibit a strong form of incompatibility of states and measurements, and use this to construct a version of the BB84 protocol that works in any non-classical GPT.

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