Quantum

Journal: Quantum

Publisher

Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften

ISSN

2521-327X

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Publications1 - 10 of 48

Device-independent quantum key distribution from generalized CHSH inequalities
Sekatski, Pavel; Bancal, Jean-Daniel; Valcarce, Xavier; et al. (2021)
Quantum
Device-independent quantum key distribution aims at providing security guarantees even when using largely uncharacterised devices. In the simplest scenario, these guarantees are derived from the CHSH score, which is a simple linear combination of four correlation functions. We here derive a security proof from a generalisation of the CHSH score, which effectively takes into account the individual values of two correlation functions. We show that this additional information, which is anyway available in practice, allows one to get higher key rates than with the CHSH score. We discuss the potential advantage of this technique for realistic photonic implementations of device-independent quantum key distribution.
Gravitational time dilation as a resource in quantum sensing
Cepollaro, Carlo; Giacomini, Flaminia; Paris, Matteo G.A. (2023)
Quantum
Atomic clock interferometers are a valuable tool to test the interface between quantum theory and gravity, in particular via the measurement of gravitational time dilation in the quantum regime. Here, we investigate whether gravitational time dilation may be also used as a resource in quantum information theory. In particular, we show that for a freely falling interferometer and for a Mach-Zehnder interferometer, the gravitational time dilation may enhance the precision in estimating the gravitational acceleration for long interferometric times. To this aim, the interferometric measurements should be performed on both the path and the clock degrees of freedom.
The refined quantum extremal surface prescription from the asymptotic equipartition property
Wang, Jinzhao (2022)
Quantum
Information theoretic ideas have provided numerous insights in the progress of fundamental physics, especially in our pursuit of quantum gravity. In particular, the holographic entanglement entropy is a very useful tool in studying AdS/CFT, and its efficacy is manifested in the recent black hole page curve calculation. On the other hand, the one-shot information theoretic entropies, such as the smooth min/max-entropies, are less discussed in AdS/CFT. They are however more fundamental entropy measures from the quantum information perspective and should also play pivotal roles in holography. We combine the technical methods from both quantum information and quantum gravity to put this idea on firm grounds. In particular, we study the quantum extremal surface (QES) prescription that was recently revised to highlight the significance of one-shot entropies in characterizing the QES phase transition. Motivated by the asymptotic equipartition property (AEP), we derive the refined quantum extremal surface prescription for fixed-area states via a novel AEP replica trick, demonstrating the synergy between quantum information and quantum gravity. We further prove that, when restricted to pure bulk marginal states, such corrections do not occur for the higher Renyi entropies of a boundary subregion in fixed-area states, meaning they always have sharp QES transitions. Our path integral derivation suggests that the refinement applies beyond AdS/CFT, and we confirm it in a black hole toy model by showing that the Page curve, for a black hole in superposition of two radiation stages, receives a large correction that is consistent with the refined QES prescription.
Relational superposition measurements with a material quantum ruler
Wang, Hui; Giacomini, Flaminia; Nori, Franco; et al. (2024)
Quantum
In physics, it is crucial to identify operational measurement procedures to give physical meaning to abstract quantities. There has been significant effort to define time operationally using quantum systems, but the same has not been achieved for space. Developing an operational procedure to obtain information about the location of a quantum system is particularly important for a theory combining general relativity and quantum theory, which cannot rest on the classical notion of spacetime. Here, we take a first step towards this goal, and introduce a model to describe an extended material quantum system working as a position measurement device. Such a "quantum ruler" is composed of N harmonically interacting dipoles and serves as a (quantum) reference system for the position of another quantum system. We show that we can define a quantum measurement procedure corresponding to the "superposition of positions", and that by performing this measurement we can distinguish when the quantum system is in a coherent or incoherent superposition in the position basis. The model is fully relational, because the only meaningful variables are the relative positions between the ruler and the system, and the measurement is expressed in terms of an interaction between the measurement device and the measured system.
Concentration bounds for quantum states and limitations on the QAOA from polynomial approximations
Anshu, Anurag; Metger, Tony (2023)
Quantum
We prove concentration bounds for the following classes of quantum states: (i) output states of shallow quantum circuits, answering an open question from [16]; (ii) injective matrix product states; (iii) output states of dense Hamiltonian evolution, i.e. states of the form eˡᴴ⁽ᵖ⁾ ... Hˡᴴ⁽¹⁾ |ψ₀⟩ for any n-qubit product state |ψ₀⟩, where each H⁽ᶦ⁾ can be any local commuting Hamiltonian satisfying a norm constraint, including dense Hamiltonians with interactions between any qubits. Our proofs use polynomial approximations to show that these states are close to local operators. This implies that the distribution of the Hamming weight of a computational basis measurement (and of other related observables) concentrates. An example of (iii) are the states produced by the quantum approximate optimisation algorithm (QAOA). Using our concentration results for these states, we show that for a random spin model, the QAOA can only succeed with negligible probability even at super-constant level p = o(loglogn) assuming a strengthened version of the so-called overlap gap property. This gives the first limitations on the QAOA on dense instances at super-constant level, improving upon the recent result [BGMZ22].
The first law of general quantum resource theories
Sparaciari, Carlo; del Rio, Lídia; Scandolo, Carlo M.; et al. (2020)
Quantum
We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. We thus have a set of laws for general quantum resource theories, which generalise the laws of thermodynamics. We first test this approach on thermodynamics with multiple conservation laws, and then apply it to the theory of local operations under energetic restrictions.
Composably secure device-independent encryption with certified deletion
Kundu, Srijita; Tan, Ying Zhe Ernest (2023)
Quantum
We study the task of encryption with certified deletion (ECD) introduced by Broadbent and Islam (2020), but in a device-independent setting: we show that it is possible to achieve this task even when the honest parties do not trust their quantum devices. Moreover, we define security for the ECD task in a composable manner and show that our ECD protocol satisfies conditions that lead to composable security. Our protocol is based on device-independent quantum key distribution (DIQKD), and in particular the parallel DIQKD protocol based on the magic square non-local game, given by Jain, Miller and Shi (2020). To achieve certified deletion, we use a property of the magic square game observed by Fu and Miller (2018), namely that a two-round variant of the game can be used to certify deletion of a single random bit. In order to achieve certified deletion security for arbitrarily long messages from this property, we prove a parallel repetition theorem for two-round non-local games, which may be of independent interest.
The complexity of quantum support vector machines
Gentinetta, Gian; Thomsen, Arne; Sutter, David; et al. (2024)
Quantum
Quantum support vector machines employ quantum circuits to define the kernel function. It has been shown that this approach offers a provable exponential speedup compared to any known classical algorithm for certain data sets. The training of such models corresponds to solving a convex optimization problem either via its primal or dual formulation. Due to the probabilistic nature of quantum mechanics, the training algorithms are affected by statistical uncertainty, which has a major impact on their complexity. We show that the dual problem can be solved in O(M⁴.⁶⁷/ε²) quantum circuit evaluations, where M denotes the size of the data set and ε the solution accuracy compared to the ideal result from exact expectation values, which is only obtainable in theory. We prove under an empirically motivated assumption that the kernelized primal problem can alternatively be solved in O(min{M²/ε⁶, 1/ε¹⁰}) evaluations by employing a generalization of a known classical algorithm called Pegasos. Accompanying empirical results demonstrate these analytical complexities to be essentially tight. In addition, we investigate a variational approximation to quantum support vector machines and show that their heuristic training achieves considerably better scaling in our experiments.
Cutting circuits with multiple two-qubit unitaries
Schmitt, Lukas; Piveteau, Christophe; Sutter, David (2025)
Quantum
Quasiprobabilistic cutting techniques allow us to partition large quantum circuits into smaller sub circuits by replacing non-local gates with probabilistic mixtures of local gates. The cost of this method is a sampling overhead that scales exponentially in the number of cuts. It is crucial to determine the minimal cost for gate cutting and to understand whether allowing for classical communication between sub circuits can improve the sampling overhead. In this work, we derive a closed formula for the optimal sampling overhead for cutting an arbitrary number of two-qubit unitaries and provide the corresponding decomposition. We find that cutting several arbitrary two-qubit unitaries together is cheaper than cutting them individually and classical communication does not give any advantage.
Algorithmic Error Mitigation Scheme for Current Quantum Processors
Suchsland, Philippe; Tacchino, Francesco; Fischer, Mark H.; et al. (2021)
Quantum
We present a hardware agnostic error mitigation algorithm for near term quantum processors inspired by the classical Lanczos method. This technique can reduce the impact of different sources of noise at the sole cost of an increase in the number of measurements to be performed on the target quantum circuit, without additional experimental overhead. We demonstrate through numerical simulations and experiments on IBM Quantum hardware that the proposed scheme significantly increases the accuracy of cost functions evaluations within the framework of variational quantum algorithms, thus leading to improved ground state calculations for quantum chemistry and physics problems beyond state-of-the-art results.

Publications1 - 10 of 48

Journal: Quantum

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