1,721,015 research outputs found
Gaussian optimizers and other topics in quantum information
Full text linkGaussian input states have long been conjectured to minimize the output von Neumann entropy of quantum Gaussian channels for fixed input entropy. We prove the quantum Entropy Power Inequality, that provides an extremely tight lower bound to this minimum output entropy, but is not saturated by Gaussian states, hence it is not sufficient to prove their optimality. Passive states are diagonal in the energy eigenbasis and their eigenvalues decrease as the energy increases. We prove that for any one-mode Gaussian channel, the output generated by a passive state majorizes the output generated by any state with the same spectrum, hence it has a lower entropy. Then, the minimizers of the output entropy of a Gaussian channel for fixed input entropy are passive states. We exploit this result to prove that Gaussian states minimize the output entropy of the one-mode attenuator for fixed input entropy. This result opens the way to the multimode generalization, that permits to determine both the classical capacity region of the Gaussian quantum degraded broadcast channel and the triple trade-off region of the quantum attenuator. Still in the context of Gaussian quantum information, we determine the classical information capacity of a quantum Gaussian channel with memory effects. Moreover, we prove that any one-mode linear trace-preserving not necessarily positive map preserving the set of Gaussian states is a quantum Gaussian channel composed with the phase-space dilatation. These maps are tests for certifying that a given quantum state does not belong to the convex hull of Gaussian states. Our result proves that phase-space dilatations are the only test of this kind. In the context of quantum statistical mechanics, we prove that requiring thermalization of a quantum system in contact with a heat bath for any initial uncorrelated state with a well-defined temperature implies the Eigenstate Thermalization Hypothesis for the system-bath Hamiltonian. Then, the ETH constitutes the unique criterion to decide whether a given system-bath dynamics always leads to thermalization. In the context of relativistic quantum information, we prove that any measurement able to distinguish a coherent superposition of two wavepackets of a massive or charged particle from the corresponding incoherent statistical mixture must require a minimum time. This bound provides an indirect evidence for the existence of quantum gravitational radiation and for the necessity of quantizing gravity
Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states
Full text linkWe prove that the entanglement entropy of any pure initial state of a bipartite bosonic quantum system grows linearly in time with respect to the dynamics induced by any unstable quadratic Hamiltonian. The growth rate does not depend on the initial state and is equal to the sum of certain Lyapunov exponents of the corresponding classical dynamics. This paper generalizes the findings of [Bianchi et al., JHEP 2018, 25 (2018)], which proves the same result in the special case of Gaussian initial states. Our proof is based on a recent generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum systems [De Palma et al., arXiv:2105.05627]. This technique allows us to extend our result to generic mixed initial states, with the squashed entanglement providing the right generalization of the entanglement entropy. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems, including certain quantum field theory models
A non-perturbative argument for the non-abelian Higgs mechanism
Full text linkThe evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gaugeThe evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. © 2013 Elsevier Inc
Quantum Optimal Transport: Quantum Channels and Qubits
No full textThese notes are based on the lectures given by the second author at the
School on Optimal Transport on Quantum Structures at Erd\"os Center in
September 2022. The focus of the exposition is on two recently introduced
approaches on quantum optimal transport: one based on quantum channels as
generalized transport plans, the other based on the notion of
Hamming-Wasserstein distance of order 1 on multiple-qubit systems. The material
is presented in an elementary manner with a focus on the finite-dimensional
setting
Quantum Concentration Inequalities and Equivalence of the Thermodynamical Ensembles: An Optimal Mass Transport Approach
No full textWe prove new concentration inequalities for quantum spin systems which apply to any local observable measured on any product state or on any state with exponentially decaying correlations. Our results do not require the spins to be arranged in a regular lattice, and cover the case of observables that contain terms acting on spins at arbitrary distance. Moreover, we introduce a local W1 distance, which quantifies the distinguishability of two states with respect to local observables. We prove a transportation-cost inequality stating that the local W1 distance between a generic state and a state with exponentially decaying correlations is upper bounded by a function of their relative entropy. Finally, we apply such inequality to prove the equivalence between the canonical and microcanonical ensembles of quantum statistical mechanics and the weak eigenstate thermalization hypothesis for the Hamiltonians whose Gibbs states have exponentially decaying correlations
Uncertainty relations with quantum memory for the Wehrl entropy
Full text linkWe prove two new fundamental uncertainty relations with quantum memory for the Wehrl entropy. The first relation applies to the bipartite memory scenario. It determines the minimum conditional Wehrl entropy among all the quantum states with a given conditional von Neumann entropy and proves that this minimum is asymptotically achieved by a suitable sequence of quantum Gaussian states. The second relation applies to the tripartite memory scenario. It determines the minimum of the sum of the Wehrl entropy of a quantum state conditioned on the first memory quantum system with the Wehrl entropy of the same state conditioned on the second memory quantum system and proves that also this minimum is asymptotically achieved by a suitable sequence of quantum Gaussian states. The Wehrl entropy of a quantum state is the Shannon differential entropy of the outcome of a heterodyne measurement performed on the state. The heterodyne measurement is one of the main measurements in quantum optics and lies at the basis of one of the most promising protocols for quantum key distribution. These fundamental entropic uncertainty relations will be a valuable tool in quantum information and will, for example, find application in security proofs of quantum key distribution protocols in the asymptotic regime and in entanglement witnessing in quantum optics
The Wehrl entropy has Gaussian optimizers
Full text linkWe determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel that associates with a quantum state its Husimi Q representation is asymptotically equivalent to the Gaussian quantum-limited amplifier with infinite amplification parameter. This equivalence also permits to determine the p→q norms of the aforementioned quantum-classical channel in the two particular cases of one mode and p=q and prove that they are achieved by thermal Gaussian states. The same equivalence permits to prove that the Husimi Q representation of a one-mode passive state (i.e., a state diagonal in the Fock basis with eigenvalues decreasing as the energy increases) majorizes the Husimi Q representation of any other one-mode state with the same spectrum, i.e., it maximizes any convex functional
Classical shadows meet quantum optimal mass transport
Full text linkClassical shadows constitute a protocol to estimate the expectation values of a collection of M observables acting on O(1) qubits of an unknown n-qubit state with a number of measurements that is independent of n and that grows only logarithmically with M. We propose a local variant of the quantum Wasserstein distance of order 1 of [De Palma et al., IEEE Trans. Inf. Theory 67, 6627 (2021)] and prove that the classical shadow obtained measuring O(log n) copies of the state to be learned constitutes an accurate estimate with respect to the proposed distance. We apply the results to quantum generative adversarial networks, showing that quantum access to the state to be learned can be useful only when some prior information on such state is available.29 page
Classical capacity of Gaussian thermal memory channels
Full text linkThe classical capacity of phase-invariant Gaussian channels has been recently determined under the assumption that such channels are memoryless. In this work we generalize this result by deriving the classical capacity of a model of quantum memory channel, in which the output states depend on the previous input states. In particular we extend the analysis of Lupo et al. [Phys. Rev. Lett. 104, 030501 (2010) and Phys. Rev. A 82, 032312 (2010)] from quantum limited channels to thermal attenuators and thermal amplifiers. Our result applies in many situations in which the physical communication channel is affected by nonzero memory and by thermal noise.The classical capacity of phase-invariant Gaussian channels has been recently determined under the assumption that such channels are memoryless. In this work we generalize this result by deriving the classical capacity of a model of quantum memory channel, in which the output states depend on the previous input states. In particular we extend the analysis of Lupo et al. [Phys. Rev. Lett. 104, 030501 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.030501 and Phys. Rev. A 82, 032312 (2010)PLRAAN1050-294710.1103/PhysRevA.82.032312] from quantum limited channels to thermal attenuators and thermal amplifiers. Our result applies in many situations in which the physical communication channel is affected by nonzero memory and by thermal noise
Passive states optimize the output of bosonic Gaussian quantum channels
Full text linkAn ordering between the quantum states emerging from a single-mode gauge-covariant bosonic Gaussian channel is proved. Specifically, we show that within the set of input density matrices with the same given spectrum, the element passive with respect to the Fock basis (i.e., diagonal with decreasing eigenvalues) produces an output, which majorizes all the other outputs emerging from the same set. When applied to pure input states, our finding includes as a special case the result of Mari et al., Nat. Comm. 5, 3826 (2014) which implies that the output associated to the vacuum majorizes the others
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