Dahlem center for complex quantum systems

Preprints

BibTeX:

	@unpublished{nowforever,, title
	= {

Preprints
}, year =
	2030 }

Zhao Liu, Gunnar Möller and Emil J. Bergholtz
Lattice Genons
arXiv:1702.05115v1 [cond-mat.str-el].

[Abstract] [URL]

Abstract: Topological degeneracy is, together with fractionalization, the hallmark of topological order. While fractionalization has been demonstrated both theoretically and in laboratories leading to deep insights into our basic understanding of matter, there has been no corresponding success in tracking the evolution of ground-state degeneracy due to the lack of tractable microscopic models with arbitrarily tunable topology of space. In this work however, by computer simulations, we show that lattice versions of multicomponent fractional quantum Hall systems are novel playgrounds to fill this void. With wormhole-like defects that connect separated "universes" of different components, thus changing the global topology of space, we observe a nontrivial dependence of ground-state degeneracy on the number of defects, equivalent to adding exotic non-Abelian quasiparticles called "genons" proposed recently in terms of effective topological field theory. We identify a number of different lattice genons in both Abelian and non-Abelian phases, with quantum dimensions exceeding those of fundamental quasiparticles in the host states, and provide a promising platform to study their intriguing behavior.

BibTeX:

	@unpublished{1702.05115v1,
	author =
	Zhao Liu, Gunnar Möller and Emil J. Bergholtz, title
	= Lattice Genons, year =
	2017, note
	= arXiv:1702.05115v1 [cond-mat.str-el], url =
	http://arxiv.org/abs/1702.05115v1 }

Vir B. Bulchandani, Romain Vasseur, Christoph Karrasch and Joel E. Moore
Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
arXiv:1702.06146v1 [cond-mat.stat-mech].

[Abstract] [URL]

Abstract: Quantum integrable systems, such as the interacting Bose gas in one dimension and the XXZ quantum spin chain, have an extensive number of local conserved quantities that endow them with exotic thermalization and transport properties. We review recently introduced hydrodynamic approaches for such integrable systems in detail and extend them to finite times and arbitrary initial conditions. We then discuss how such methods can be applied to describe non-equilibrium steady states involving ballistic heat and spin currents. In particular, we show that the spin Drude weight in the XXZ chain, previously accessible only by heuristic Bethe ansatz techniques, may be evaluated from hydrodynamics in very good agreement with density-matrix renormalization group calculations. This agreement is a strong check on the equivalence between the generalized hydrodynamics resulting from the infinite set of conservation laws in this model on the one hand, and the Bethe-Boltzmann equation in terms of the pseudo-momentum distribution on the other.

BibTeX:

	@unpublished{1702.06146v1,
	author =
	Vir B. Bulchandani, Romain Vasseur, Christoph Karrasch and Joel E. Moore, title
	= Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain, year =
	2017, note
	= arXiv:1702.06146v1 [cond-mat.stat-mech], url =
	http://arxiv.org/abs/1702.06146v1 }

Henrik Wilming, Rodrigo Gallego and Jens Eisert
Axiomatic characterization of the quantum relative entropy and free energy
arXiv:1702.08473v1 [quant-ph].

[Abstract] [URL]

Abstract: Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: i) Continuity in the first argument, ii) the validity of the data-processing inequality, iii) additivity under tensor products, and iv) super-additivity. This observation has immediate implications for quantum thermodynamics, which we discuss. Specifically, we demonstrate that, under reasonable restrictions, the free energy is singled out as a measure of athermality. In particular, we consider an extended class of Gibbs-preserving maps as free operations in a resource-theoretic framework, in which a catalyst is allowed to build up correlations with the system at hand. The free energy is the only extensive and continuous function that is monotonic under such free operations.

BibTeX:

	@unpublished{1702.08473v1,
	author =
	Henrik Wilming, Rodrigo Gallego and Jens Eisert, title
	= Axiomatic characterization of the quantum relative entropy and free
energy, year =
	2017, note
	= arXiv:1702.08473v1 [quant-ph], url =
	http://arxiv.org/abs/1702.08473v1 }

Manuel Laubach, Johannes Reuther, Ronny Thomale and Stephan Rachel
Three-band Hubbard model for Na$_2$IrO$_3$: Topological insulator, zigzag antiferromagnet, and Kitaev-Heisenberg material
arXiv:1701.04896v1 [cond-mat.str-el].

[Abstract] [URL]

Abstract: Na$_2$IrO$_3$ was one of the first materials proposed to feature the Kane-Mele type topological insulator phase. Contemporaneously it was claimed that the very same material is in a Mott insulating phase which is described by the Kitaev-Heisenberg (KH) model. First experiments indeed revealed Mott insulating behavior in conjunction with antiferromagnetic long-range order. Further refined experiments established antiferromagnetic order of zigzag type which is not captured by the KH model. Since then several extensions and modifications of the KH model were proposed in order to describe the experimental findings. Here we suggest that adding charge fluctuations to the KH model represents an alternative explanation of zigzag antiferromagnetism. Moreover, a phenomenological three-band Hubbard model unifies all the pieces of the puzzle: topological insulator physics for weak and KH model for strong electron-electron interactions as well as a zigzag antiferromagnet at intermediate interaction strength.

BibTeX:

	@unpublished{1701.04896v1,
	author =
	Manuel Laubach, Johannes Reuther, Ronny Thomale and Stephan Rachel, title
	= Three-band Hubbard model for Na$_2$IrO$_3$: Topological insulator, zigzag antiferromagnet, and Kitaev-Heisenberg material, year =
	2017, note
	= arXiv:1701.04896v1 [cond-mat.str-el], url =
	http://arxiv.org/abs/1701.04896v1 }

U. Las Heras, R. Di Candia, K. G. Fedorov, F. Deppe, M. Sanz and E. Solano
Quantum Illumination Unveils Cloaking
arXiv:1611.10280v1 [quant-ph].

[Abstract] [URL]

Abstract: In quantum illumination entangled light is employed to enhance the detection accuracy of an object when compared with the best classical protocol. On the other hand, cloaking is a stealth technology based on covering a target with a material deflecting the light around the object to avoid its detection. Here, we propose a quantum illumination protocol especially adapted to quantum microwave technology which, by seizing weaknesses in current cloaking techniques, allows for a $3$ dB improvement in the detection of a cloaked target. Finally, we study the minimal efficiency required by the photocounter for which the quantum illumination protocol still shows a gain with respect to the classical protocol.

BibTeX:

	@unpublished{1611.10280v1,
	author =
	U. Las Heras, R. Di Candia, K. G. Fedorov, F. Deppe, M. Sanz and E. Solano, title
	= Quantum Illumination Unveils Cloaking, year =
	2016, note
	= arXiv:1611.10280v1 [quant-ph], url =
	http://arxiv.org/abs/1611.10280v1 }

Daniel Litinski, Piet W. Brouwer and Michele Filippone
The Interacting Mesoscopic Capacitor Out of Equilibrium
arXiv:1612.04822v1 [cond-mat.mes-hall].

[Abstract] [URL]

Abstract: We consider the full non-equilibrium response of a mesoscopic capacitor in the large transparency limit, exactly solving a model with electron-electron interactions appropriate for a cavity in the quantum Hall regime. For a cavity coupled to the electron reservoir via an ideal point contact, we show that the response to any time-dependent gate voltage $V_{\rm g}(t)$ is strictly linear in $V_{\rm g}$. We analyze the charge and current response to a sudden gate voltage shift, and find that this response is not captured by a simple circuit analogy. In particular, in the limit of strong interactions a sudden change in the gate voltage leads to the emission of a sequence of multiple charge pulses, the width and separation of which are controlled by the charge-relaxation time $\tau_{\rm c} = h C_{\rm g}/e^2$ and the time of flight $\tau_{\rm f}$. We also consider the effect of a finite reflection amplitude in the point contact, which leads to non-linear-in-gate-voltage corrections to the charge and current response.

BibTeX:

	@unpublished{1612.04822v1,
	author =
	Daniel Litinski, Piet W. Brouwer and Michele Filippone, title
	= The Interacting Mesoscopic Capacitor Out of Equilibrium, year =
	2016, note
	= arXiv:1612.04822v1 [cond-mat.mes-hall], url =
	http://arxiv.org/abs/1612.04822v1 }

Elina Locane and Piet W. Brouwer
Current-induced switching of magnetic molecules on topological insulator surfaces
arXiv:1612.02711v1 [cond-mat.mes-hall].

[Abstract] [URL]

Abstract: Electrical currents at the surface or edge of a topological insulator are intrinsically spin-polarized. We show that such surface/edge currents can be used to switch the orientation of a molecular magnet weakly coupled to the surface or edge of a topological insulator. For the edge of a two-dimensional topological insulator as well as for the surface of a three-dimensional topological insulator the application of a well-chosen surface/edge current can lead to a complete polarization of the molecule if the molecule's magnetic anisotropy axis is appropriately aligned with the current direction. For a generic orientation of the molecule a nonzero but incomplete polarization is obtained. We calculate the probability distribution of the magnetic states and the switching rates as a function of the applied current.

BibTeX:

	@unpublished{1612.02711v1,
	author =
	Elina Locane and Piet W. Brouwer, title
	= Current-induced switching of magnetic molecules on topological insulator
surfaces, year =
	2016, note
	= arXiv:1612.02711v1 [cond-mat.mes-hall], url =
	http://arxiv.org/abs/1612.02711v1 }

M. L. Baez and J. Reuther
Numerical treatment of spin systems with unrestricted spin length $S$: A functional renormalization group study
arXiv:1612.05074v2 [cond-mat.str-el].

[Abstract] [URL]

Abstract: We develop a generalized pseudo-fermion functional renormalization group (PFFRG) approach that can be applied to arbitrary Heisenberg models with spins ranging from the quantum case $S=1/2$ to the classical limit $S\rightarrow\infty$. Within this framework, spins of magnitude $S$ are realized by implementing $M=2S$ copies of spin-1/2 degrees of freedom on each lattice site. We confirm that even without explicitly projecting onto the highest spin sector of the Hilbert space, ground states tend to select the largest possible local spin magnitude. This justifies the average treatment of the pseudo fermion constraint in previous spin-1/2 PFFRG studies. We apply this method to the antiferromagnetic $J_1$-$J_2$ honeycomb Heisenberg model with nearest neighbor $J_1>0$ and second neighbor $J_2>0$ interactions. Mapping out the phase diagram in the $J_2/J_1$-$S$ plane we find that upon increasing $S$ quantum fluctuations are rapidly decreasing. In particular, already at $S=1$ we find no indication for a magnetically disordered phase. In the limit $S\rightarrow\infty$, the known phase diagram of the classical system is exactly reproduced. More generally, we prove that for $S\rightarrow\infty$ the PFFRG approach is identical to the Luttinger-Tisza method.

BibTeX:

	@unpublished{1612.05074v2,
	author =
	M. L. Baez and J. Reuther, title
	= Numerical treatment of spin systems with unrestricted spin length $S$: A
functional renormalization group study, year =
	2016, note
	= arXiv:1612.05074v2 [cond-mat.str-el], url =
	http://arxiv.org/abs/1612.05074v2 }

A. Steffens, C. Riofrio, W. McCutcheon, B. A. Bell, A. McMillan, J. G. Rarity and J. Eisert
Experimentally exploring compressed sensing quantum tomography
arXiv:1611.01189 [quant-ph].

[Abstract] [URL]

Abstract: In the light of the progress in quantum technologies, the task of verifying the correct functioning of processes and obtaining accurate tomographic information about quantum states becomes increasingly important. Compressed sensing, a machinery derived from the theory of signal processing, has emerged as a feasible tool to perform robust and significantly more resource-economical quantum state tomography for intermediate-sized quantum systems. In this work, we provide a comprehensive analysis of compressed sensing tomography in the regime in which tomographically complete data is available with reliable statistics from experimental observations of a multi-mode photonic architecture. Due to the fact that the data is known with high statistical significance, we are in a position to systematically explore the quality of reconstruction depending on the number of employed measurement settings, randomly selected from the complete set of data, and on different model assumptions. We present and test a complete prescription to perform efficient compressed sensing and are able to reliably use notions of model selection and cross-validation to account for experimental imperfections and finite counting statistics. Thus, we establish compressed sensing as an effective tool for quantum state tomography, specifically suited for photonic systems.

BibTeX:

	@unpublished{Steffens2016,
	author =
	A. Steffens, C. Riofrio, W. McCutcheon, B. A. Bell, A. McMillan, J. G. Rarity and J. Eisert, title
	= Experimentally exploring compressed sensing quantum tomography, year =
	2016, note
	= arXiv:1611.01189 [quant-ph], url =
	https://arxiv.org/abs/1611.01189 }

Gleb Skorobagatko, Anton Bruch, Silvia Viola Kusminskiy and Alessandro Romito
Effect of interactions on quantum limited detectors
arXiv:1609.07281 [cond-mat.mes-hall].

[Abstract] [URL]

Abstract: We consider the effect of electron-electron interactions on a voltage biased quantum point contact in the tunneling regime used as a detector of a nearby qubit. We model the leads of the quantum point contact as Luttinger liquids, incorporate the effects of finite temperature and analyze the detection-induced decoherence rate and the detector efficiency, $Q$. We find that interactions generically reduce the induced decoherence along with the detector's efficiency, and strongly affect the relative strength of the decoherence induced by tunneling and that induced by interactions with the local density. With increasing interaction strength, the regime of quantum limited detection ($Q=1$) is shifted to increasingly lower temperatures or higher bias voltages respectively. For small to moderate interaction strengths, $Q$ is a monotonously decreasing function of temperature as in the non-interacting case. Surprisingly, for sufficiently strong interactions we identify an intermediate temperature regime where the efficiency of the detector increases with rising temperature.

BibTeX:

	@unpublished{Skorobagatko2016,
	author =
	Gleb Skorobagatko, Anton Bruch, Silvia Viola Kusminskiy and Alessandro Romito, title
	= Effect of interactions on quantum limited detectors, year =
	2016, note
	= arXiv:1609.07281 [cond-mat.mes-hall], url =
	https://arxiv.org/abs/1609.07281 }

Patrick Rebentrost, Adrian Steffens and Seth Lloyd
Quantum singular value decomposition of non-sparse low-rank matrices
arXiv:1607.05404v1 [quant-ph].

[Abstract] [URL]

Abstract: In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors to be found quantum mechanically in a time exponentially faster in the dimension of the matrix than known classical algorithms. The method extends to non-Hermitian and non-square matrices via embedding matrices. In the context of the generic singular value decomposition of a matrix, we discuss the Procrustes problem of finding a closest isometry to a given matrix.

BibTeX:

	@unpublished{1607.05404v1,
	author =
	Patrick Rebentrost, Adrian Steffens and Seth Lloyd, title
	= Quantum singular value decomposition of non-sparse low-rank matrices, year =
	2016, note
	= arXiv:1607.05404v1 [quant-ph], url =
	http://arxiv.org/abs/1607.05404v1 }

E. Onorati, O. Buerschaper, M. Kliesch, W. Brown, A. H. Werner and J. Eisert
Mixing properties of stochastic quantum Hamiltonians
arXiv:1606.01914 [quant-ph].

[Abstract] [URL]

Abstract: Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and quantum information theory. In this work, we present a framework describing the mixing properties of continuous-time unitary evolutions originating from local Hamiltonians having time-fluctuating terms, reflecting a Brownian motion on the unitary group. The induced stochastic time evolution is shown to converge to a unitary design. As a first main result, we present bounds to the mixing time. By developing tools in representation theory, we analytically derive an expression for a local k-th moment operator that is entirely independent of k, giving rise to approximate unitary k-designs and quantum tensor product expanders. As a second main result, we introduce tools for proving bounds on the rate of decoupling from an environment with random quantum processes. By tying the mathematical description closely with the more established one of random quantum circuits, we present a unified picture for analysing local random quantum and classes of Markovian dissipative processes, for which we discuss applications.

BibTeX:

	@unpublished{Onorati2016,
	author =
	E. Onorati, O. Buerschaper, M. Kliesch, W. Brown, A. H. Werner and J. Eisert, title
	= Mixing properties of stochastic quantum Hamiltonians, year =
	2016, note
	= arXiv:1606.01914 [quant-ph], url =
	https://arxiv.org/abs/1606.01914 }

Björn Sbierski, Maximilian Trescher, Emil J. Bergholtz and Piet W. Brouwer
Disordered double Weyl node: Comparison of transport and density-of-states calculations
arXiv:1606.06941 [cond-mat.mes-hall].

[Abstract] [URL]

Abstract: Double Weyl nodes are topologically protected band crossing points which carry chiral charge $\pm2$. They are stabilized by $C_{4}$ point group symmetry and are predicted to occur in $\mathrm{SrSi_{2}}$ or $\mathrm{HgCr_{2}Se_{4}}$. We study their stability and physical properties in the presence of a disorder potential. We investigate the density of states and the quantum transport properties at the nodal point. We find that, in contrast to their counterparts with unit chiral charge, double Weyl nodes are unstable to any finite amount of disorder and give rise to a diffusive phase, in agreement with predictions of Goswami and Nevidomskyy [Phys. Rev. B 92, 214504 (2015)] and Bera, Sau, and Roy [Phys. Rev. B 93, 201302(R) (2016)]. However, for finite system sizes a crossover between pseudodiffusive and diffusive quantum transport can be observed.

BibTeX:

	@unpublished{Sbierski2016a,
	author =
	Björn Sbierski, Maximilian Trescher, Emil J. Bergholtz and Piet W. Brouwer, title
	= Disordered double Weyl node: Comparison of transport and density-of-states calculations, year =
	2016, note
	= arXiv:1606.06941 [cond-mat.mes-hall], url =
	https://arxiv.org/abs/1606.06941 }

H. Wilming, M. J. Kastoryano, A. H. Werner and J. Eisert
Emergence of spontaneous symmetry breaking in dissipative lattice systems
arXiv:1602.01108 [quant-ph].

[Abstract] [URL]

Abstract: A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analogue of such a theory. Specifically, we consider local dissipative dynamics preparing a steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive fluctuations in a local order parameter. We show that for all such processes satisfying detailed balance, there exist metastable symmetry-breaking states, i.e., states that become stationary in the thermodynamic limit and give a finite value to the order parameter. We give results both for discrete and continuous symmetries and explicitly show how to construct the symmetry-breaking states. Our results show in a simple way that, in large systems, local dissipative dynamics satisfying detailed balance cannot uniquely and efficiently prepare states with extensive fluctuations with respect to local operators. We discuss the implications of our results for quantum simulators and dissipative state preparation.

BibTeX:

	@unpublished{Wilming2016,
	author =
	H. Wilming, M. J. Kastoryano, A. H. Werner and J. Eisert, title
	= Emergence of spontaneous symmetry breaking in dissipative lattice systems, year =
	2016, note
	= arXiv:1602.01108 [quant-ph], url =
	http://arxiv.org/abs/1602.01108 }

Juan Bermejo-Vega and Kevin C. Zatloukal
Abelian Hypergroups and Quantum Computation
arXiv:1509.05806 [quant-ph].

[Abstract] [URL]

Abstract: Motivated by a connection, described here for the first time, between the hidden normal subgroup problem (HNSP) and abelian hypergroups (algebraic objects that model collisions of physical particles), we develop a stabilizer formalism using abelian hypergroups and an associated classical simulation theorem (a la Gottesman-Knill). Using these tools, we develop the first provably efficient quantum algorithm for finding hidden subhypergroups of nilpotent abelian hypergroups and, via the aforementioned connection, a new, hypergroup-based algorithm for the HNSP on nilpotent groups. We also give efficient methods for manipulating non-unitary, non-monomial stabilizers and an adaptive Fourier sampling technique of general interest.

BibTeX:

	@unpublished{Bermejo-Vega2015,
	author =
	Juan Bermejo-Vega and Kevin C. Zatloukal, title
	= Abelian Hypergroups and Quantum Computation, year =
	2015, note
	= arXiv:1509.05806 [quant-ph], url =
	http://arxiv.org/abs/1509.05806 }

Netanel H. Lindner, Aaron Farrell, Eran Lustig, Gil Refael and Felix von Oppen
Lighting up topological insulators: large surface photocurrents from magnetic superlattices
arXiv:1403.0010v2 [cond-mat.mes-hall].

[Abstract] [URL]

Abstract: The gapless surface states of topological insulators (TI) can potentially be used to detect and harvest low-frequency infrared light. Nonetheless, it was shown that significant surface photocurrents due to light with frequency below the bulk gap are rather hard to produce. Here we demonstrate that a periodic magnetic pattern added to the surface dramatically enhances surface photocurrents in TI's. Moreover, the sensitivity of this set-up to the wavelength of the incident light can be optimized by tuning the geometry of the magnetic pattern. The ability to produce substantial photocurrents on TI surfaces from mid-range and far-infrared light could be used in photovoltaic applications, as well as for detection of micrometer wavelength radiation. For light of wavelength greater than 15$\mu$m we estimate that at room temperature, a detector based on the effect we describe can have a specific detectivity as high as 10$^7$ cm$\sqrt{\text{Hz}}$/W (i.e. 10$^9$ Jones). The device can therefore operate at much larger wavelengths than existing infrared detectors, while maintaining a comparable figure of merit.er wavelength radiation.

BibTeX:

	@unpublished{1403.0010v2,
	author =
	Netanel H. Lindner, Aaron Farrell, Eran Lustig, Gil Refael and Felix von Oppen, title
	= Lighting up topological insulators: large surface photocurrents from
magnetic superlattices, year =
	2014, note
	= arXiv:1403.0010v2 [cond-mat.mes-hall], url =
	http://arxiv.org/abs/1403.0010v2 }

C. Gogolin, M. Kliesch, L. Aolita and J. Eisert
Boson-Sampling in the light of sample complexity
arXiv:1306.3995 [quant-ph].

[Abstract] [URL]

Abstract: Boson-Sampling is a classically computationally hard problem that can - in principle - be efficiently solved with quantum linear optical networks. Very recently, a rush of experimental activity has ignited with the aim of developing such devices as feasible instances of quantum simulators. Even approximate Boson-Sampling is believed to be hard with high probability if the unitary describing the optical network is drawn from the Haar measure. In this work we show that in this setup, with probability exponentially close to one in the number of bosons, no symmetric algorithm can distinguish the Boson-Sampling distribution from the uniform one from fewer than exponentially many samples. This means that the two distributions are operationally indistinguishable without detailed a priori knowledge. We carefully discuss the prospects of efficiently using knowledge about the implemented unitary for devising non-symmetric algorithms that could potentially improve upon this. We conclude that due to the very fact that Boson-Sampling is believed to be hard, efficient classical certification of Boson-Sampling devices seems to be out of reach.

BibTeX:

	@unpublished{2013arXiv1306.3995G,
	author =
	C. Gogolin, M. Kliesch, L. Aolita and J. Eisert, title
	= Boson-Sampling in the light of sample complexity, year =
	2013, note
	= arXiv:1306.3995 [quant-ph], url =
	http://arxiv.org/abs/1306.3995 }

F. Caravelli, F. Markopoulou, A. Riera and L. Sindoni
Quenches and lattice simulators for particle creation
arXiv:1212.1981 [gr-qc].

[Abstract] [URL]

Abstract: In this paper we propose a framework for simulating thermal particle production in condensed matter systems. The procedure we describe can be realized by means of a quantum quench of a parameter in the model. In order to support this claim, we study quadratic fermionic systems in one and two dimensions by means of analytical and numerical techniques. In particular, we are able to show that a class of observables associated to Unruh--de Witt detectors are very relevant for this type of setup and that exhibit approximate thermalization.

BibTeX:

	@unpublished{2012arXiv1212.1981C,
	author =
	F. Caravelli, F. Markopoulou, A. Riera and L. Sindoni, title
	= Quenches and lattice simulators for particle creation, year =
	2012, note
	= arXiv:1212.1981 [gr-qc], url =
	http://arxiv.org/abs/1212.1981 }

M. Ohliger, V. Nesme, D. Gross, Y.-K. Liu and J. Eisert
Continuous-variable quantum compressed sensing
arXiv:1111.0853v2 [quant-ph].

[Abstract] [URL]

Abstract: We introduce a novel method to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. The method is general enough to allow for measurements from a continuous family, and is also applicable to continuous-variable states. As a technical result, this work generalizes quantum compressed sensing to the situation where the measured observables are taken from a so-called tight frame (rather than an orthonormal basis) --- hence covering most realistic measurement scenarios. As an application, we discuss the reconstruction of quantum states of light from homodyne detection and other types of measurements, and we present simulations that show the advantage of the proposed compressed sensing technique over present methods. Finally, we introduce a method to construct a certificate which guarantees the success of the reconstruction with no assumption on the state, and we show how slightly more measurements give rise to "universal" state reconstruction that is highly robust to noise.

BibTeX:

	@unpublished{Ohliger2011,
	author =
	M. Ohliger, V. Nesme, D. Gross, Y.-K. Liu and J. Eisert, title
	= Continuous-variable quantum compressed sensing, year =
	2011, note
	= arXiv:1111.0853v2 [quant-ph], url =
	http://arxiv.org/abs/1111.0853 }

2017

BibTeX:

	@unpublished{20172018,, title
	= {

Preprints
}, year =
	2017 }

Adrian Steffens, Patrick Rebentrost, Iman Marvian, Jens Eisert and Seth Lloyd
An efficient quantum algorithm for spectral estimation
New Journal of Physics 19(3), 033005 (2017).