arXiv subjects

Vittorio Giovannetti

Publications and source records attributed to Vittorio Giovannetti.

At least 163 records · Page 9Linked to original sources

arXiv2017

Multimode Gaussian optimizers for the Wehrl entropy and quantum Gaussian channels

We prove in the multimode scenario a fundamental relation between the Wehrl and the von Neumann entropy, stating that the minimum Wehrl entropy among all the quantum states with a given von Neumann entropy is achieved by thermal Gaussian states. We also prove that thermal Gaussian input states minimize the output von Neumann entropy of multimode quantum Gaussian attenuators, amplifiers and phase-contravariant channels among all the input states diagonal in some product basis and with a given entropy. This result constitutes a major step towards the proof of the same property for generic input states, which is still an open conjecture. This conjecture is necessary to determine the maximum communication rates for the triple trade-off coding and broadcast communication with the Gaussian quantum-limited attenuator. Finally, we prove that the tensor product of n identical geometric input probability distributions minimizes the output Shannon entropy of the n-mode thinning among all the input probability distributions with a given entropy.

math-ph↗

arXiv2017

Gaussian states minimize the output entropy of one-mode quantum Gaussian channels

We prove the longstanding conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the Entropy Power Inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p->q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.

quant-ph↗

arXiv2017

Cut-and-paste restoration of entanglement transmission

The distribution of entangled quantum systems among two or more nodes of a network is a key task at the basis of quantum communication, quantum computation and quantum cryptography. Unfortunately the transmission lines used in this procedure can introduce so much perturbations and noise in the transmitted signal that prevent the possibility of restoring quantum correlations in the received messages either by means of encoding optimization or by exploiting local operations and classical communication. In this work we present a procedure which allows one to improve the performance of some of these channels. The mechanism underpinning this result is a protocol which we dub cut-and-paste, as it consists in extracting and reshuffling the sub-components of these communication lines, which finally succeed in "correcting each other". The proof of this counterin- tuitive phenomenon, while improving our theoretical understanding of quantum entanglement, has also a direct application in the realization of quantum information networks based on imperfect and highly noisy communication lines. A quantum optics experiment, based on the transmission of single-photon polarization states, is also presented which provides a proof-of-principle test of the proposed protocol.

quant-ph↗

arXiv2017

Estimating Temperature via Sequential Measurements

We study the efficiency of estimation procedures where the temperature of an external bath is indirectly recovered by monitoring the transformations induced on a probing system that is put in thermal contact with the bath. In particular we compare the performances of sequential measurement schemes where the probe is initialized only once and measured repeatedly during its interaction with the bath, with those of measure & re-prepare approaches where instead, after each interaction-and-measurement stage, the probe is reinitialized into the same fiduciary state. From our analysis it is revealed that the sequential approach, while being in general not capable of providing the best accuracy achievable, is nonetheless more versatile with respect to the choice of the initial state of the probe, yielding on average smaller indetermination levels.

quant-ph↗

arXiv2017

Lindbladian purification

In a recent work [D. K. Burgarth et al., Nat. Commun. 5, 5173 (2014)] it was shown that a series of frequent measurements can project the dynamics of a quantum system onto a subspace in which the dynamics can be more complex. In this subspace even full controllability can be achieved, although the controllability over the system before the projection is very poor since the control Hamiltonians commute with each other. We can also think of the opposite: any Hamiltonians of a quantum system, which are in general noncommutative with each other, can be made commutative by embedding them in an extended Hilbert space, and thus the dynamics in the extended space becomes trivial and simple. This idea of making noncommutative Hamiltonians commutative is called "Hamiltonian purification." The original noncommutative Hamiltonians are recovered by projecting the system back onto the original Hilbert space through frequent measurements. Here we generalize this idea to open-system dynamics by presenting a simple construction to make Lindbladians, as well as Hamiltonians, commutative on a larger space with an auxiliary system. We show that the original dynamics can be recovered through frequently measuring the auxiliary system in a non-selective way. Moreover, we provide a universal pair of Lindbladians which describes an "accessible" open quantum system for generic system sizes. This allows us to conclude that through a series of frequent non-selective measurements a nonaccessible open quantum system generally becomes accessible. This sheds further light on the role of measurement backaction on the control of quantum systems.

quant-ph↗

arXiv2017

Optimal quantum state discrimination via nested binary measurements

A method to compute the optimal success probability of discrimination of N arbitrary quantum states is presented, based on the decomposition of any N-outcome measurement into sequences of nested two-outcome ones. In this way the optimization of the measurement operators can be carried out in successive steps, optimizing first the binary measurements at the deepest nesting level and then moving on to those at higher levels. We obtain an analytical expression for the maximum success probability after the first optimization step and examine its form for the specific case of N=3,4 states of a qubit. In this case, at variance with previous proposals, we are able to provide a compact expression for the success probability of any set of states, whose numerical optimization is straightforward; the results thus obtained highlight some lesser-known features of the discrimination problem.

quant-ph↗

arXiv2016

Gaussian States Minimize the Output Entropy of the One-Mode Quantum Attenuator

We prove that Gaussian thermal input states minimize the output von Neumann entropy of the one-mode Gaussian quantum-limited attenuator for fixed input entropy. The Gaussian quantum-limited attenuator models the attenuation of an electromagnetic signal in the quantum regime. The Shannon entropy of an attenuated real-valued classical signal is a simple function of the entropy of the original signal. A striking consequence of energy quantization is that the output von Neumann entropy of the quantum-limited attenuator is no more a function of the input entropy alone. The proof starts from the majorization result of De Palma et al., IEEE Trans. Inf. Theory 62, 2895 (2016), and is based on a new isoperimetric inequality. Our result implies that geometric input probability distributions minimize the output Shannon entropy of the thinning for fixed input entropy. Moreover, our result opens the way to the multimode generalization, that permits to determine both the triple trade-off region of the Gaussian quantum-limited attenuator and the classical capacity region of the Gaussian degraded quantum broadcast channel.

quant-ph↗

arXiv2016

Multi-Phase Hadamard receivers for classical communication on lossy bosonic channels

A scheme for transferring classical information over a lossy bosonic channel is proposed by generalizing the proposal presented in Phys. Rev. Lett. 106, 240502 (2011) by Guha. It employs codewords formed by products of coherent states of fixed mean photon number with multiple phases which, through a passive unitary transformation, reduce to a Pulse-Position Modulation code with multiple pulse phases. The maximum information rate achievable with optimal, yet difficult to implement, detection schemes is computed and shown to saturate the classical capacity of the channel in the low energy regime. An easy to implement receiver based on a conditional Dolinar detection scheme is also proposed finding that, while suboptimal, it allows for improvements in an intermediate photon-number regime with respect to previous proposals.

quant-ph↗

arXiv2016

Modulated phases of graphene quantum Hall polariton fluids

There is growing experimental interest in coupling cavity photons to the cyclotron resonance excitations of electron liquids in high-mobility semiconductor quantum wells or graphene sheets. These media offer unique platforms to carry out fundamental studies of exciton-polariton condensation and cavity quantum electrodynamics in a regime in which electron-electron interactions are expected to play a pivotal role. Focusing on graphene, we present a theoretical study of the impact of electron-electron interactions on a quantum Hall polariton fluid, that is a fluid of magneto-excitons resonantly coupled to cavity photons. We show that electron-electron interactions are responsible for an instability of graphene integer quantum Hall polariton fluids towards a modulated phase. We demonstrate that this phase can be detected by measuring the collective excitation spectra, which soften at a characteristic wave vector of the order of the inverse magnetic length.

cond-mat.mes-hall↗

arXiv2016

Passive states as optimal inputs for single-jump lossy quantum channels

The passive states of a quantum system minimize the average energy among all the states with a given spectrum. We prove that passive states are the optimal inputs of single-jump lossy quantum channels. These channels arise from a weak interaction of the quantum system of interest with a large Markovian bath in its ground state, such that the interaction Hamiltonian couples only consecutive energy eigenstates of the system. We prove that the output generated by any input state $ρ$ majorizes the output generated by the passive input state $ρ_0$ with the same spectrum of $ρ$. Then, the output generated by $ρ$ can be obtained applying a random unitary operation to the output generated by $ρ_0$. This is an extension of De Palma et al., IEEE Trans. Inf. Theory 62, 2895 (2016), where the same result is proved for one-mode bosonic Gaussian channels. We also prove that for finite temperature this optimality property can fail already in a two-level system, where the best input is a coherent superposition of the two energy eigenstates.

quant-ph↗

arXiv2016

Quantum memories with zero-energy Majorana modes and experimental constraints

In this work we address the problem of realizing a reliable quantum memory based on zero-energy Majorana modes in the presence of experimental constraints on the operations aimed at recovering the information. In particular, we characterize the best recovery operation acting only on the zero-energy Majorana modes and the memory fidelity that can be therewith achieved. In order to understand the effect of such restriction, we discuss two examples of noise models acting on the topological system and compare the amount of information that can be recovered by accessing either the whole system, or the zero-modes only, with particular attention to the scaling with the size of the system and the energy gap. We explicitly discuss the case of a thermal bosonic environment inducing a parity-preserving Markovian dynamics in which the introduced memory fidelity decays exponentially in time, independent from system size, thus showing the impossibility to retrieve the information by acting on the zero-modes only. We argue, however, that even in the presence of experimental limitations, the Hamiltonian gap is still beneficial to the storage of information.

quant-ph↗

arXiv2016

Achieving the Holevo bound via a bisection decoding protocol

We present a new decoding protocol to realize transmission of classical information through a quantum channel at asymptotically maximum capacity, achieving the Holevo bound and thus the optimal communication rate. At variance with previous proposals, our scheme recovers the message bit by bit, making use of a series "yes-no" measurements, organized in bisection fashion, thus determining which codeword was sent in log(N) steps, N being the number of codewords.

quant-ph↗

arXiv2016

Coherent-state discrimination via non-heralded probabilistic amplification

A scheme for the detection of low-intensity optical coherent signals was studied which uses a probabilistic amplifier operated in the non-heralded version, as the underlying non-linear operation to improve the detection efficiency. This approach allows us to improve the statistics by keeping track of all possible outcomes of the amplification stage (including failures). When compared with an optimized Kennedy receiver, the resulting discrimination success probability we obtain presents a gain up to ~1.85% and it approaches the Helstrom bound appreciably faster than the Dolinar receiver, when employed in an adaptive strategy. We also notice that the advantages obtained can be ultimately associated with the fact that, in the high gain limit, the non-heralded version of the probabilistic amplifier induces a partial dephasing which preserves quantum coherence among low energy eigenvectors while removing it elsewhere. A proposal to realize such transformation based on an optical cavity implementation is presented.

quant-ph↗

arXiv2016

Local quantum thermal susceptibility

Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties originate from averaging procedures which smoothen out local details. While undoubtedly successful, elegant and formally correct, this approach carries over an operational problem: what is the precision at which such variables are inferred, when technical/practical limitations restrict our capabilities to local probing? Here we introduce the local quantum thermal susceptibility, a quantifier for the best achievable accuracy for temperature estimation via local measurements. Our method relies on basic concepts of quantum estimation theory, providing an operative strategy to address the local thermal response of arbitrary quantum systems at equilibrium. At low temperatures it highlights the local distinguishability of the ground state from the excited sub-manifolds, thus providing a method to locate quantum phase transitions.

quant-ph↗

arXiv2016

Universal Control Induced by Noise

On the basis of the quantum Zeno effect it has been recently shown [D. K. Burgarth et al., Nat. Commun. 5, 5173 (2014)] that a strong amplitude damping process applied locally on a part of a quantum system can have a beneficial effect on the dynamics of the remaining part of the system. Quantum operations that cannot be implemented without the dissipation become achievable by the action of the strong dissipative process. Here we generalize this idea by identifying decoherence-free subspaces (DFS's) as the subspaces in which the dynamics becomes more complex. Applying methods from quantum control theory we characterize the set of reachable operations within the DFS's. We provide three examples which become fully controllable within the DFS's while the control over the original Hilbert space in the absence of dissipation is trivial. In particular, we show that the (classical) Ising Hamiltonian is turned into a Heisenberg Hamiltonian by strong collective decoherence, which provides universal quantum computation within the DFS's. Moreover we perform numerical gate optimization to study how the process fidelity scales with the noise strength. As a byproduct a subsystem fidelity which can be applied in other optimization problems for open quantum systems is developed.

quant-ph↗

arXiv2016

Optimal processes for probabilistic work extraction beyond the second law

According to the second law of thermodynamics, for every transformation performed on a system which is in contact with an environment of fixed temperature, the extracted work is bounded by the decrease of the free energy of the system. However, in a single realization of a generic process, the extracted work is subject to statistical fluctuations which may allow for probabilistic violations of the previous bound. We are interested in enhancing this effect, i.e. we look for thermodynamic processes that maximize the probability of extracting work above a given arbitrary threshold. For any process obeying the Jarzynski identity, we determine an upper bound for the work extraction probability that depends also on the minimum amount of work that we are willing to extract in case of failure, or on the average work we wish to extract from the system. Then we show that this bound can be saturated within the thermodynamic formalism of quantum discrete processes composed by sequences of unitary quenches and complete thermalizations. We explicitly determine the optimal protocol which is given by two quasi-static isothermal transformations separated by a finite unitary quench.

quant-ph↗

arXiv2016

Passive states optimize the output of bosonic Gaussian quantum channels

An ordering between the quantum states emerging from a single mode gauge-covariant bosonic Gaussian channel is proven. 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 A. Mari, et al., Nat. Comm. 5, 3826 (2014) which implies that the output associated to the vacuum majorizes the others.

quant-ph↗

arXiv2016

Necessity of Eigenstate Thermalization

Under the Eigenstate Thermalization Hypothesis (ETH), quantum-quenched systems equilibrate towards canonical, thermal ensembles. While at first glance the ETH might seem a very strong hypothesis, we show that it is indeed not only sufficient but also necessary for thermalization. More specifically, we consider systems coupled to baths with well-defined macroscopic temperature and show that whenever all product states thermalize then the ETH must hold. Our result definitively settles the question of determining whether a quantum system has a thermal behaviour, reducing it to checking whether its Hamiltonian satisfies the ETH.

quant-ph↗