Speaker: Wen-Long Ma (Institute of Semiconductors, Chinese Academy of Sciences)
The relation between projective measurements and generalized quantum measurements is a fundamental problem in quantum physics, and clarifying this issue is also important to quantum technologies. While it has been intuitively known that projective measurements can be constructed from sequential generalized or weak measurements, there is still lack of a proof of this hypothesis in general cases. Here we rigorously prove it from the perspective of quantum channels. We show that projective measurements naturally arise from sequential generalized measurements in the asymptotic limit. Specifically, a selective projective measurement arises from a set of typical sequences of sequential generalized measurements. We provide an explicit scheme to construct projective measurements of a quantum system with sequential generalized quantum measurements. Remarkably, a single ancilla qubit is sufficient to mediate a sequential weak measurement for constructing arbitrary projective measurements of a generic system. As an example, we present a protocol to measure the modular excitation number of a bosonic mode with an ancilla qubit.
Speaker: Christoph Dittel (University of Freiburg)
Indistinguishability is the essential ingredient for many-body interference — a purely
quantum mechanical interference effect between many identical bosonic or fermionic
particles that can be exploited for a variety of applications, ranging from simulations with
ultracold atoms to photonic quantum information processing. In this talk I give an
introduction into this fascinating many-body property. Starting from its consequences on
interference effects, I show how partial particle distinguishability entails a wave-particle
duality relation on the many-body level. Moreover, I discuss how partial distinguishability
due to mixedness — in the particles’ internal degrees of freedom — induces many-body
decoherence whose strength increases exponentially in the number of constituents.
Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this view is undermined by the fact that there exist operational theories which exhibit nontrivial uncertainty relations but which are consistent with the classical worldview insofar as they admit of a generalized-noncontextual ontological model. This prompts the question of what aspects of uncertainty relations, if any, cannot be realized in this way and so constitute evidence of genuine nonclassicality. We here consider uncertainty relations describing the tradeoff between the predictability of a pair of binary-outcome measurements (e.g., measurements of Pauli X and Pauli Z observables in quantum theory). We show that, for a class of theories satisfying a particular symmetry property, the functional form of this predictability tradeoff is constrained by noncontextuality to be below a linear curve. Because qubit quantum theory has the relevant symmetry property, the fact that it has a quadratic tradeoff between these predictabilities is a violation of this noncontextual bound, and therefore constitutes an example of how the functional form of an uncertainty relation can witness contextuality. We also deduce the implications for a selected group of operational foils to quantum theory and consider the generalization to three measurements.
Based on https://arxiv.org/abs/2207.11779.
Quantum value for a family of I3322-like Bell functionals
In this work, we study a three-parameter family of Bell functionals in a bipartite scenario with 3 measurement settings per party and 2 outcomes per measurement. The members of this family can be thought of as variations of the well-known I3322 functional, the only one in this scenario corresponding to a tight Bell inequality if we take aside the CHSH inequality. An analysis of their largest value achievable by quantum realisations (quantum value) naturally splits the set into two branches, and for the first of them, we show that this value is given by a simple function of the parameters defining the functionals. In this case we completely characterise the realisations attaining the optimal value and show that these functionals can be used to self-test any partially entangled state of two qubits. The optimal measurements, however, are not unique and form a one-parameter family of qubit measurements. Within the second branch, the quantum value presents a more complex dependence on the parameters defining the functionals and is studied numerically, identifying first the regions in parameter space where two-qubit systems suffice to approach the quantum value. The remainder of the branch includes the I3322 functional, for which a particular sequence of finite-dimensional realisations introduced by K. Pál and T. Vértesi is known to numerically attain the quantum value in the limit of infinite local dimension. We study the performance of these special strategies beyond the I3322 case and analyse the optimal solutions in those cases where they succeed in approaching the quantum value.
Strongly coupled quantum Otto cycle with single qubit bath
We discuss a model of a unitary evolution of two-qubits where the joint Hamiltonian is so chosen that one of the qubits acts as a bath and thermalizes the other qubit which is acting as the system. The corresponding master equation for the system, for a specific choice of parameters, takes the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form with constant coefficients representing pumping and damping of a single qubit system. Based on this model we construct an Otto cycle connected to a single qubit bath and study its thermodynamic properties. Our analysis goes beyond the conventional weak coupling scenario and illustrates the effects of finite bath including non-Markovianity. We find closed form expressions for efficiency (coefficient of performance), power (cooling power) for heat engine regime (refrigerator regime) for different modifications of the joint Hamiltonian.
Quantum Singular Value Transformation – A Unifying framework of quantum algorithms
Speaker: András Gilyén (Alfréd Rényi Institute of Mathematics)
Abstract An n-qubit quantum circuit performs a unitary operation on an exponentially large, 2^n-dimensional, Hilbert space, which is a major source of quantum speed-ups. We show how Quantum Singular Value Transformation can directly harness the advantages of exponential dimensionality by applying polynomial transformations to the singular values of a block of a unitary operator. The transformations are realized by quantum circuits with a very simple structure – typically using only a constant number of ancilla qubits – leading to optimal algorithms with appealing constant factors. We show that this framework allows describing and unifying many quantum algorithms on a high level, and enables remarkably concise proofs for many prominent quantum algorithms, ranging from optimal Hamiltonian simulation to quantum linear equation solving (i.e., the HHL algorithm) and advanced amplitude amplification techniques. Finally, we also prove a quantum lower bound on spectral transformations.
Gaussian states, Kähler structures and an entanglement duality
Speaker: Robert H. Jonsson (Wallenberg Initiative on Networks and Quantum Information, Nordita (Stockholm)
Gaussian quantum states play a central role in many branches of physics – from quantum optics, to condensed matter and quantum field theory. In this talk, I aim to showcase the strength of the Kähler structure formalism for Gaussian states by discussing a recent result on the entanglement structure of supersymmetric (SUSY) bosonic and fermionic Gaussian states .
Mathematically, Gaussian states can be defined in terms of Kähler structures on classical phase space. In fact, this approach has proven to be very powerful: It yields a formalism which is both practical for applications, clearly captures the structure and geometry of Gaussian states, adapts to discrete and continuous settings and, moreover, can treat bosons and fermions simultaneously.
To exemplify this, we will consider the basic example of a free SUSY system. This is a pair of one bosonic and one fermionic quadratic hamiltonian which is generated by a supercharge and, therefore, is isospectral. Not only does the Kähler structure formalism parallelly capture the Gaussian ground states and their entanglement structure of both the bosonic and the fermionic part. Moreover, it allows us to derive an appealing entanglement duality between bosonic and fermionic subsystems , and to interpret it in terms of phase space geometry and its physical implications. Time permitting, as a special application, we consider topological insulators and superconductors and their SUSY partners, discussing the recently derived classification of supercharges in this context .
 Jonsson, Robert H., Lucas Hackl, and Krishanu Roychowdhury. “Entanglement Dualities in Supersymmetry.” Physical Review Research 3, no. 2 (June 16, 2021): 023213.
 Gong, Zongping, Robert H. Jonsson, and Daniel Malz. “Supersymmetric Free Fermions and Bosons: Locality, Symmetry, and Topology.” Physical Review B 105, no. 8 (February 24, 2022): 085423.
Nonlocal games and operator algebras: solution spaces and robust self-testing in the quantum commuting model
Date: Wednesday, June 29, 2022
Host: Quantum Information and Quantum Computing Working Group (CTP PAS)
Speaker: Alexander Frei (University of Copenhagen)
We begin by recalling quantum strategies in the context of nonlocal games, and their description in terms of the state space on the full group algebra of certain free groups. With this description at hand, we then examine the quantum value and quantum strategies for the following prominent classes of games:
1) The tilted CHSH game.
We showcase here how to compute the quantum value at first for the classical CHSH game using some basic operator algebraic techniques. For the more general tilted CHSH game, we then invoke some more elaborate classification of representations which then allows us to reduce the quantum value to an optimisation problem. These allow us moreover to deduce the solution space of optimal states and their uniqueness, in the sense that there will be only a single optimal state giving rise to the optimal quantum value, and which in particular entails the usual self-testing result. We moreover find previously unknown phase transitions on the uniqueness of optimal states when varying the parameters for the tilted CHSH game.
2) The Mermin-Peres magic square and magic pentagram game.
As before, we also note here uniqueness of optimal states, which in these two examples is a basically familiar result.
Based on uniqueness of optimal states as entire states on full group algebras, we then discuss robust self-testing in the quantum commuting model in the context of above discussed games. We do so by building upon ideas found in work by Mancinska, Prakash and Schafhauser. We then demonstrate this on the classes (1) and (2) above, and so find a first robust self-testing result in the quantum commuting model.
The talk is based on joint work with Azin Shahiri.
I’ll review the concept of expressing the two basic notions of Riemannian geometry using spectral methods and Wodzicki residue over the algebra of pseudodifferential operators. This approach admits generalizations to the framework of noncommutative geometry. Based on joint work with L.Dabrowski and P.Zalecki.
Algebraic Bethe Circuits
Date: Wednesday, June 15, 2022
Host: Quantum Information and Quantum Computing Working Group (CTP PAS)
Speaker: Diego García-Martín (TII, Abu Dhabi, UAE)
The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA to unitary form, for its direct implementation on a quantum computer. This is achieved by distilling the non-unitary R matrices that make up the ABA into unitaries using the QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method in the spin- 1 2 XX and XXZ models. We show that using this approach one can efficiently prepare eigenstates of the XX model on a quantum computer with quantum resources that match previous state-of-the-art approaches. We run numerical simulations, preparing eigenstates of the XXZ model for systems of up to 24 qubits and 12 magnons. Furthermore, we run small-scale error-mitigated implementations on the IBM quantum computers, including the preparation of the ground state for the XX and XXZ models in 4 sites. Finally, we derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.