arXiv subjects

J. Eisert

Publications and source records attributed to J. Eisert.

At least 127 records · Page 7Linked to original sources

arXiv2010

Limitations of quantum computing with Gaussian cluster states

We discuss the potential and limitations of Gaussian cluster states for measurement-based quantum computing. Using a framework of Gaussian projected entangled pair states (GPEPS), we show that no matter what Gaussian local measurements are performed on systems distributed on a general graph, transport and processing of quantum information is not possible beyond a certain influence region, except for exponentially suppressed corrections. We also demonstrate that even under arbitrary non-Gaussian local measurements, slabs of Gaussian cluster states of a finite width cannot carry logical quantum information, even if sophisticated encodings of qubits in continuous-variable (CV) systems are allowed for. This is proven by suitably contracting tensor networks representing infinite-dimensional quantum systems. The result can be seen as sharpening the requirements for quantum error correction and fault tolerance for Gaussian cluster states, and points towards the necessity of non-Gaussian resource states for measurement-based quantum computing. The results can equally be viewed as referring to Gaussian quantum repeater networks.

quant-ph↗

arXiv2010

Quantum computational webs

We introduce the notion of quantum computational webs: These are quantum states universal for measurement-based computation which can be built up from a collection of simple primitives. The primitive elements - reminiscent of building blocks in a construction kit - are (i) states on a one-dimensional chain of systems ("computational quantum wires") with the power to process one logical qubit and (ii) suitable couplings which connect the wires to a computationally universal "web". All elements are preparable by nearest-neighbor interactions in a single pass - a type of operation well-suited for a number of physical architectures. We provide a complete classification of qubit wires. This is first instance where a physically well-motivated class of universal resources can be fully understood. Finally, we sketch possible realizations in superlattices, and explore the power of coupling mechanisms based on Ising or exchange-interactions.

quant-ph↗

arXiv2010

Probing local relaxation of cold atoms in optical superlattices

In the study of relaxation processes in coherent non-equilibrium dynamics of quenched quantum systems, ultracold atoms in optical superlattices with periodicity two provide a very fruitful test ground. In this work, we consider the dynamics of a particular, experimentally accessible initial state prepared in a superlattice structure evolving under a Bose-Hubbard Hamiltonian in the entire range of interaction strengths, further investigating the issues raised in Ref. [Phys. Rev. Lett. 101, 063001 (2008)]. We investigate the relaxation dynamics analytically in the non interacting and hard core bosonic limits, deriving explicit expressions for the dynamics of certain correlation functions, and numerically for finite interaction strengths using the time-dependent density-matrix renormalization (t-DMRG) approach. We can identify signatures of local relaxation that can be accessed experimentally with present technology. While the global system preserves the information about the initial condition, locally the system relaxes to the state having maximum entropy respecting the constraints of the initial condition. For finite interaction strengths and finite times, the relaxation dynamics contains signatures of the relaxation dynamics of both the non-interacting and hard core bosonic limits.

cond-mat.stat-mech↗

arXiv2010

Area laws for the entanglement entropy - a review

Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: The entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such "area laws" for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium we review the current status of area laws in these fields. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation, and disordered systems, non-equilibrium situations, classical correlation concepts, and topological entanglement entropies are discussed. A significant proportion of the article is devoted to the quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. We discuss matrix-product states, higher-dimensional analogues, and states from entanglement renormalization and conclude by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations.

quant-ph↗

arXiv2009

Entanglement quantification from incomplete measurements: Applications using photon-number-resolving weak homodyne detectors

The certificate of success for a number of important quantum information processing protocols, such as entanglement distillation, is based on the difference in the entanglement content of the quantum states before and after the protocol. In such cases, effective bounds need to be placed on the entanglement of non-local states consistent with statistics obtained from local measurements. In this work, we study numerically the ability of a novel type of homodyne detector which combines phase sensitivity and photon-number resolution to set accurate bounds on the entanglement content of two-mode quadrature squeezed states without the need for full state tomography. We show that it is possible to set tight lower bounds on the entanglement of a family of two-mode degaussified states using only a few measurements. This presents a significant improvement over the resource requirements for the experimental demonstration of continuous-variable entanglement distillation, which traditionally relies on full quantum state tomography.

quant-ph↗

arXiv2009

Gently modulating opto-mechanical systems

We introduce a framework of opto-mechanical systems that are driven with a mildly amplitude modulated light field, but that are not subject to classical feedback or squeezed input light. We find that in such a system one can achieve large degrees of squeezing of a mechanical micromirror signifying quantum properties of opto-mechanical systems - without the need of any feedback and control, and within parameters reasonable in experimental settings. Entanglement dynamics is shown of states following classical quasi-periodic orbits in their first moments. We discuss the complex time dependence of the modes of a cavity-light field and a mechanical mode in phase space. Such settings give rise to certifiable quantum properties within experimental conditions feasible with present technology.

quant-ph↗

arXiv2009

Measuring Measurement: Theory and Practice

Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well specified assumptions. The formalism is completely general and can be applied to a wide range of detectors

quant-ph↗

arXiv2009

Exact relaxation in a class of non-equilibrium quantum lattice systems

A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we study a setting where relaxation to a steady state is exact, namely for the Bose-Hubbard model where the system is quenched from a Mott quantum phase to the strong superfluid regime. We find that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments, maximizing the entanglement, to a state which is different from the thermal state of the new Hamiltonian. Remarkably, in the infinite system limit this relaxation is true for all large times, and no time average is necessary. For large but finite system size we give a time interval for which the system locally "looks relaxed" up to a prescribed error. Our argument includes a central limit theorem for harmonic systems and exploits the finite speed of sound. Additionally, we show that for all periodic initial configurations, reminiscent of charge density waves, the system relaxes locally. We sketch experimentally accessible signatures in optical lattices as well as implications for the foundations of quantum statistical mechanics.

cond-mat.stat-mech↗

arXiv2009

Most quantum states are too entangled to be useful as computational resources

It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs a sufficient amount of entanglement for this speedup to be manifest. In measurement-based quantum computing (MBQC), the need for a highly entangled initial state is particularly obvious. Defying this intuition, we show that quantum states can be too entangled to be useful for the purpose of computation. We prove that this phenomenon occurs for a dramatic majority of all states: the fraction of useful n-qubit pure states is less than exp(-n^2). Computational universality is hence a rare property in quantum states. This work highlights a new aspect of the question concerning the role entanglement plays for quantum computational speed-ups. The statements remain true if one allows for certain forms of post-selection and also cover the notion of CQ-universality. We identify scale-invariant states resulting from a MERA construction as likely candidates for physically relevant states subject to this effect.

quant-ph↗

arXiv2009

A proposed testbed for detector tomography

Measurement is the only part of a general quantum system that has yet to be characterized experimentally in a complete manner. Detector tomography provides a procedure for doing just this; an arbitrary measurement device can be fully characterized, and thus calibrated, in a systematic way without access to its components or its design. The result is a reconstructed POVM containing the measurement operators associated with each measurement outcome. We consider two detectors, a single-photon detector and a photon-number counter, and propose an easily realized experimental apparatus to perform detector tomography on them. We also present a method of visualizing the resulting measurement operators.

quant-ph↗

arXiv2009

Supersonic quantum communication

When locally exciting a quantum lattice model, the excitation will propagate through the lattice. The effect is responsible for a wealth of non-equilibrium phenomena, and has been exploited to transmit quantum information through spin chains. It is a commonly expressed belief that for local Hamiltonians, any such propagation happens at a finite "speed of sound". Indeed, the Lieb-Robinson theorem states that in spin models, all effects caused by a perturbation are limited to a causal cone defined by a constant speed, up to exponentially small corrections. In this work we show that for translationally invariant bosonic models with nearest-neighbor interactions, this belief is incorrect: We prove that one can encounter excitations which accelerate under the natural dynamics of the lattice and allow for reliable transmission of information faster than any finite speed of sound. The effect is only limited by the model's range of validity (eventually by relativity). It also implies that in non-equilibrium dynamics of strongly correlated bosonic models far-away regions may become quickly entangled, suggesting that their simulation may be much harder than that of spin chains even in the low energy sector.

quant-ph↗

arXiv2008

Assessing non-Markovian dynamics

We investigate what a snapshot of a quantum evolution - a quantum channel reflecting open system dynamics - reveals about the underlying continuous time evolution. Remarkably, from such a snapshot, and without imposing additional assumptions, it can be decided whether or not a channel is consistent with a time (in)dependent Markovian evolution, for which we provide computable necessary and sufficient criteria. Based on these, a computable measure of `Markovianity' is introduced. We discuss how the consistency with Markovian dynamics can be checked in quantum process tomography. The results also clarify the geometry of the set of quantum channels with respect to being solutions of time (in)dependent master equations.

quant-ph↗

arXiv2008

Multi-mode bosonic Gaussian channels

A complete analysis of multi-mode bosonic Gaussian channels is proposed. We clarify the structure of unitary dilations of general Gaussian channels involving any number of bosonic modes and present a normal form. The maximum number of auxiliary modes that is needed is identified, including all rank deficient cases, and the specific role of additive classical noise is highlighted. By using this analysis, we derive a canonical matrix form of the noisy evolution of n-mode bosonic Gaussian channels and of their weak complementary counterparts, based on a recent generalization of the normal mode decomposition for non-symmetric or locality constrained situations. It allows us to simplify the weak-degradability classification. Moreover, we investigate the structure of some singular multi-mode channels, like the additive classical noise channel that can be used to decompose a noisy channel in terms of a less noisy one in order to find new sets of maps with zero quantum capacity. Finally, the two-mode case is analyzed in detail. By exploiting the composition rules of two-mode maps and the fact that anti-degradable channels cannot be used to transfer quantum information, we identify sets of two-mode bosonic channels with zero capacity.

quant-ph↗

arXiv2008

Measuring measurement

Measurement connects the world of quantum phenomena to the world of classical events. It plays both a passive role, observing quantum systems, and an active one, preparing quantum states and controlling them. Surprisingly - in the light of the central status of measurement in quantum mechanics - there is no general recipe for designing a detector that measures a given observable. Compounding this, the characterization of existing detectors is typically based on partial calibrations or elaborate models. Thus, experimental specification (i.e. tomography) of a detector is of fundamental and practical importance. Here, we present the realization of quantum detector tomography: we identify the optimal positive-operator-valued measure describing the detector, with no ancillary assumptions. This result completes the triad, state, process, and detector tomography, required to fully specify an experiment. We characterize an avalanche photodiode and a photon number resolving detector capable of detecting up to eight photons. This creates a new set of tools for accurately detecting and preparing non-classical light.

quant-ph↗

arXiv2008

Exploring local quantum many-body relaxation by atoms in optical superlattices

We establish a setting - atoms in optical superlattices with period 2 - in which one can experimentally probe signatures of the process of local relaxation and apparent thermalization in non-equilibrium dynamics without the need of addressing single sites. This opens up a way to explore the convergence of subsystems to maximum entropy states in quenched quantum many-body systems with present technology. Remarkably, the emergence of thermal states does not follow from a coupling to an environment, but is a result of the complex non-equilibrium dynamics in closed systems. We explore ways of measuring the relevant signatures of thermalization in this analogue quantum simulation of a relaxation process, exploiting the possibilities offered by optical superlattices.

cond-mat.stat-mech↗

arXiv2008

Quantum Margulis expanders

We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The quantum version shares all essential properties of the classical counterpart, e.g., it has the same degree and spectrum. Unlike previous constructions of quantum expanders, our method does not rely on non-Abelian harmonic analysis. Analogues for continuous variable systems are mentioned. Indeed, the construction seems one of the few instances where applications based on discrete and continuous phase space methods can be developed in complete analogy.

quant-ph↗

arXiv2008

Locality of dynamics in general harmonic quantum systems

The Lieb-Robinson theorem states that locality is approximately preserved in the dynamics of quantum lattice systems. Whenever one has finite-dimensional constituents, observables evolving in time under a local Hamiltonian will essentially grow linearly in their support, up to exponentially suppressed corrections. In this work, we formulate Lieb-Robinson bounds for general harmonic systems on general lattices, for which the constituents are infinite-dimensional, as systems representing discrete versions of free fields or the harmonic approximation to the Bose-Hubbard model. We consider both local interactions as well as infinite-ranged interactions, showing how corrections to locality are inherited from the locality of the Hamiltonian: Local interactions result in stronger than exponentially suppressed corrections, while non-local algebraic interactions result in algebraic suppression. We derive bounds for canonical operators, Weyl operators and outline generalization to arbitrary operators. As an example, we discuss the Klein-Gordon field, and see how the approximate locality in the lattice model becomes the exact causality in the field limit. We discuss the applicability of these results to quenched lattice systems far from equilibrium, and the dynamics of quantum phase transitions.

quant-ph↗

arXiv2008

Renormalization algorithm with graph enhancement

We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underly the density-matrix renormalization group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) may be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This new variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement (RAGE) and present numerical examples demonstrating that improvements over density-matrix renormalization group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.

quant-ph↗