Session L09: Quantum Foundations I

Breakdown of phenomenological Lindblad master equations in the strong coupling regime

The Lindblad form of the master equation has proven to be one of the most convenient ways to describe the impact of an environment interacting with the quantum systems of interest. For single quantum systems, the jump operators that characterize this interaction usually take simple forms, with clear experimental/physical interpretation. However, for coupled quantum systems the jump operators can take significantly different forms and in general the total Lindbladian for the system cannot be described by separate Lindbladians acting on the individual quantum systems. In this talk we investigate the effects of such separate, phenomenological description in optomechanical and spin-boson systems, which are particularly pronounced in the strong coupling regime and compare the results with a more realistic microscopic derivation of the master equation. We show that these approaches, phenomenological and microscopic, lead to different solutions to the model and we explore the parameter regime and conditions where these differences manifest themselves in an experiment. We propose an experiment with superconducting systems to investigate these issues and the breakdown of the phenomenological approach with increasing coupling strength.   

Entanglement classifier in chemical reactions

The Einstein, Podolsky, and Rosen (EPR) entanglement, which features the essential difference between classical and
quantum physics, has received wide theoretical and experimental attentions. Recently, the desire to understand and
create quantum entanglement between particles such as spins, photons, atoms, and molecules is fueled by the development
of quantum teleportation, quantum communication, quantum cryptography, and quantum computation.
Although most of the work has focused on showing that entanglement violates the famous Bell’s inequality and its
generalization for discrete measurements, few recent attempts focus on continuous measurement results. Here, we
have developed a general practical inequality to test entanglement for continuous measurement results, particularly
scattering of chemical reactions. After we explain how to implement this inequality to classify entanglement in
scattering experiments, we propose a specific chemical reaction to test the violation of this inequality. The method
is general and could be used to classify entanglement for continuous measurement results.   

Concurrence and Discord measurements in a Kitaev type 1D Spin chain

We present the study of concurrence and quantum discord in the ground state of 1D spins. The spins have the nearest neighbor Kitaev type interaction with the external transverse magnetic field. The system with periodic boundary condition gives the translation symmetry which simplifies the study to pairwise concurrence and discord at the odd and the even pair of sites separately. The correlation measures do not depend on the direction of the external field. They show dependence on spin length in the smaller chain but saturate quickly. The concurrence and the discord show the peak structure in the critical region but their derivatives do not show pronounced singularity to trace the phase transition of the system. The discord quantifies the correlation better as it gives finite correlation in the region where concurrence goes to zero.
Reference:
Vimalesh Kumar Vimal and V. Subrahmanyam, Phys. Rev. A 98, 052303 (2018).   

Triangle Nonlocality : genuine quantum nonlocality and quantum Finner inequality

Network nonlocality extends standard Bell nonlocality to networks, where several independent sources are distributed to several parties according to the network structure. Contrary to standard Bell Nonlocality, this problem is non convex: no efficient systematic way to tackle it is known, either for local or quantum correlations. It is only partially understood for the simplest scenarios of bilocality (extended to star-locality and nonlocality on a line). However, for scenarios with loops, e.g. the triangle network, nothing is known except examples directly deduced from the usual form of quantum nonlocality (via the violation of a standard Bell inequality). This can even be done without using inputs. The question of finding a genuine quantum violation of triangle network locality was open the last years.
In this talk, we first present a novel example of quantum nonlocality without inputs in the triangle network, which we believe represent a new form of quantum nonlocality, genuine to the triangle network. It involves both entangled qubit states and joint entangled measurements. We generalize it to qutrits shared states and any odd-cycle networks.
Then, we move to the question of the characterization of local and quantum correlations. We derive a bound, the quantum Finner inequality (already known to hold for local ressources), which we also demonstrate to hold when the sources are arbitrary no-signaling boxes which can be wired together. We generalizes this bound to all networks involving bipartite sources. We discuss it as an application for the device-independent characterization of the topology of a quantum network.
We conclude with some open questions related to quantum network nonlocality.
This talk is based on the two letters arXiv:1905.04902 and arXiv:1901.08287
  

Evolution of entanglement in collective excitations in linear atomic chains

Quantum simulation of small physically realizable systems (e.g. chains of precision placed dopant atoms in silicon) provides an opportunity to learn about many-body physics at larger scale. Electrons in 1-D atomic chains with a long range coulomb interaction support plasmonic excitations of various modes and occupations of these modes, as linear superpositions of single particle excitations. We examine the time evolution of entanglement following plasmonic excitation due to coupling between the atomic chain and dipole emitters. We compare the results for a wide range of interaction strength between the electrons, from non interacting to strongly coupled and for pumping various plasmonic modes.   

Entanglement and impropriety

We describe a classical model of quantum entanglement corresponding to spontaneous parametric downconversion. Specifically, we consider the interaction of classical stochastic vacuum modes from the zero-point field and a high intensity pump with a nonlinear optical medium. The vacuum modes are treated as proper complex Gaussian random variables and are the sole source of randomness in the model. Phase matching conditions mimic the quantum mechanical energy and momentum conservation laws and result in outgoing classical fields of maximum intensity. The resulting transformation resembles the Bogoliubuv transformation for multi-mode squeezed light, albeit with operators replaced by random variables, and yields a vector of improper complex Gaussian random variables. Using an amplitude threshold detection and post-selection measurement scheme, the degree of impropriety is found to correspond to the degree of entanglement in the corresponding quantum description.   

Tripartite information, scrambling, and the role of Hilbert space partitioning in quantum lattice models

For the characterization of the dynamics in quantum many-body systems the question how information spreads and becomes distributed over the constituent degrees of freedom is of fundamental interest. The delocalization of information under many-body dynamics has been dubbed scrambling and out-of-time-order correlators were proposed to probe this behavior. In this work we investigate the time evolution of tripartite information as a natural operator-independent measure of scrambling, which quantifies to which extent the initially localized information can only be recovered by global measurements. Studying the dynamics of quantum lattice models with tunable integrability breaking we demonstrate that in contrast to quadratic models generic interacting systems scramble information irrespective of the chosen partitioning of the Hilbert space, which justifies the characterization as scrambler. Without interactions the dynamics of tripartite information in momentum space reveals unambiguously the absence of scrambling.   

Tsirelson Polytopes and Randomness Generation

We classify the extreme points of polytopes of probability distributions in the (2,2,2) Bell-CHSH setting that are induced by a single Tsirelson bound. We also do the same for a parametrized family of polytopes obtained from two Tsirelson bounds that interact non-trivially. Such constructions can be applied to device-independent random number generation using the method of probability estimation factors (PRA 98:040304(R) (2018), arXiv:1812.07786, arXiv:1806.04553). We demonstrate a meaningful improvement in certified randomness applying the new polytopes characterized here.   

Experimental Certification of a Minimal Informationally Complete Positive Operator-Valued Measure in a Device-Independent Protocol

Minimal informationally complete positive operator-valued measures (MIC-POVMs) are a special kind of measurements in quantum theory that have the property that the statistics of their d²-outcomes are enough to reconstruct any d-dimensional quantum state. For this reason, MIC-POVMs are referred to as "standard" measurements for quantum information, and are of the utmost interest in quantum information theory and applications, where they have been shown to be the ultimate tools for quantum state tomography [1], quantum key distribution [2] and randomness certification [3], among other fields.
We report on an experiment with entangled photon pairs that certifies for the first time a MIC-POVM for qubits following a device-independent protocol. That is, modeling the state preparation and the measurement devices as black boxes and using only the statistics of the inputs and outputs.

1. J. Reháček et al., PRA 70, 052321 (2004)
2. C. A. Fuchs et al., Quantum Information and Computation 3, 377 (2003)
3. A. Acín et al., PRA 93, 040102(R) (2016)   

Many-particle interference and entanglement controlled by undetected particles

Creating and manipulating entangled states are essential for performing various tasks in quantum information science. We present a unique interferometric scheme that allows us to generate many-particle entangled states. The unique feature of the scheme is that the entangled states can be manipulated without interacting with the entangled particles [1]. We illustrate the scheme by two special cases in which Bell states and GHZ-class states are produced. The scheme also emphasizes the connection between interference and entanglement, a connection that has been of interest in fundamental physics [2-4].

[1] M. Lahiri, “Many-particle interferometry and entanglement by path identity,” Phys. Rev. A 98, 033822 (2018).
[2] M. A. Horne, A. Shimony and A. Zeilinger, “Two-Particle Interferometry,” Phys. Rev. Lett. 62, 2209 (1989).
[3] D. M. Greenberger, M. A. Horne, A. Shimony and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131 (1990).
[4] J. W. Pan, Z. B.Chen, C. Y . Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry”, Rev. Mod. Phys. 84, 777 (2012).   

Quantum State Reduction: Generalized Bipartitions from Algebras of Observables

Reduced density matrices are a powerful tool in the analysis of entanglement structure, coarse-grained dynamics, decoherence, and the emergence of classicality. While one often uses the partial trace map to produce a reduced density matrix, in many natural situations (such as limited resolution experiments) this reduction may not be achievable. We investigate the general problem of identifying how the quantum state reduces given a restriction on the observables where the appropriate state-reduction map can be defined via a generalized bipartition, which is associated with the structure of irreducible representations of the algebra generated by the restricted set of observables. One of our main technical results is a general algorithm for finding irreducible representations of matrix algebras. We demonstrate the viability of this approach with two examples of limited-resolution observables. The definition of quantum state reductions can also be extended beyond algebras of observables by a more flexible notion of bipartition, the partial bipartition, which describes coarse-grainings preserving information about a limited set (not necessarily algebra) of observables.   

Optimality in Quantum Data Compression using Dynamical Entropy

In this joint work with Duncan Wright we study lossless compression of strings of pure quantum states of indeterminate-length quantum codes which were introduced by Schumacher and Westmoreland. Past work has assumed that the strings of quantum data are prepared to be encoded in an independent and identically distributed way. We introduce the notion of quantum stochastic ensembles, allowing us to consider strings of quantum states prepared in a more general way. For any identically distributed quantum stochastic ensemble we define an associated quantum Markov chain and prove that the optimal average codeword length via lossless coding is equal to the quantum dynamical entropy of the associated quantum Markov chain.   

Experimental Test of Leggett's Inequalities with Solid-State Spins

Bell's theorem states that no local hidden variable model is compatible with quantum mechanics. Surprisingly, even if we release the locality constraint, certain nonlocal hidden variable models, such as the one proposed by Leggett, may still be at variance with the predictions of quantum physics. Here, we report an experimental test of Leggett's nonlocal model with solid-state spins in a diamond nitrogen-vacancy center. We entangle an electron spin with a surrounding weakly coupled ¹³C nuclear spin and observe that the entangled states violate Leggett-type inequalities by more than 6.4 and 10.1 standard deviations for six and eight measurement settings, respectively. Our experiment results are in full agreement with quantum predictions and render Leggett's nonlocal hidden variable model disputable with a high level of confidence.