Seminars

In quantum theory general measurements are described by so-called Positive Operator-Valued Measures (POVMs). In this work we show that in d-dimensional quantum systems an application of depolarizing noise with constant (independent of d) visibility parameter makes any POVM simulable by a randomized implementation of projective measurements that do not require any auxiliary systems to be realized. This result significantly limits the asymptotic advantage that POVMs can offer over projective measurements in various information-processing tasks, including state discrimination, shadow tomography or quantum metrology. We also apply our findings to questions originating from quantum foundations. First, we asymptotically improve the range of parameters for which Werner and isotropic states have local models for generalized measurements (by factors of d and log(d) respectively). Second, we give asymptotically tight (in terms of dimension) bounds on critical visibility for which all POVMs are jointly measurable. On the technical side we use recent advances in POVM simulation, the solution to the celebrated Kadison-Singer problem, and a method of approximate implementation of a class of “nearly rank one” POVMs by a convex combination of projective measurements, which we call dimension-deficient Naimark extension theorem. The talk will be based on upcoming joint work with Michał Kotowski (MIM UW)

The combined action of a DC bias and a microwave drive on the transport characteristic of a superconductor-quantum dot-superconductor junction is investigated. To cope with time dependent non-equilibrium effects and interactions in the quantum dot, we develop a general formalism for the dynamics of the density operator based on a particle conserving approach to superconductivity. Without invoking a broken U (1) symmetry, we identify a dynamical phase connected to the coherent transfer of Cooper pairs across the junction. In the weak coupling limit, we show that besides quasiparticle transport, proximity induced superconducting correlations manifest in anomalous pair tunneling involving the transfer of a Cooper pair. The resulting generalized master equation in presence of the microwave drive showcases the characteristic bichromatic response due to the combination of the AC Josephson effect and an AC voltage. Analytical expressions for all harmonics in the driving frequency of both the current and the reduced dot operator are given for arbitrary driving strength. For the net DC current the resulting photon assisted processes give rise to rich current-voltage characteristics. In addition to photon assisted subgap transport we find regions of total current inversion in the stability diagram. There, the junction acts as a pump with the net DC current flowing against the applied DC bias. The first harmonic of the current, being closely related to the nonlinear dynamic susceptibility of the junction, is discussed at finite applied DC bias.

The transfer of quantum information between different locations is key to many quantum information processing tasks. Whereas, the transfer of a single qubit state has been extensively investigated, the transfer of a many-body system configuration has insofar remained elusive. We address the problem of transferring the state of n interacting qubits [1]. Both the exponentially increasing Hilbert space dimension, and the presence of interactions significantly scale-up the complexity of achieving high-fidelity transfer. By employing tools from random matrix theory and using the formalism of quantum dynamical maps, we derive a general expression for the average and the variance of the fidelity of an arbitrary quantum state transfer protocol for n interacting qubits. We find that the average fidelity decreases with the amount and the type of entanglement in the sender state [2]. Finally, by adopting a weak-coupling scheme in a spin chain, we obtain the explicit conditions for high-fidelity transfer of 3 and 4 interacting qubits.
[1] Tony J G Apollaro et al, Quantum transfer of interacting qubits, 2022 New J. Phys. 24 083025
https://iopscience.iop.org/article/10.1088/1367-2630/ac86e7
[2] Tony J G Apollaro et al, Entangled States Are Harder to Transfer than Product States, Entropy 2023, 25(1), > 46;
https://doi.org/10.3390/e25010046

What does it mean for a causal structure to be “unknown”? Can we even talk about “repetitions” of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes are independent and identically distributed (i.i.d.)? Similar questions for classical probabilities, quantum states, and quantum channels are beautifully answered by “de Finetti theorems”, which connect a simple and easy-to-justify condition—symmetry under exchange—to a very particular multipartite structure: a mixture of identical states/channels. Practically, they provide the foundations for principle-based Bayesian methods, e.g., in tomography. Apart from the foundational relevance, de Finetti representations for general causal structures would be useful in the analysis of multi-time, non-Markovian processes, with applications to state-of-the-art quantum devices.

At face value, it appears that each causal structure or assumption on causal structure requires its own de Finetti theorems. Fortunately, I will show that each scenario can be mapped to a linear constraint on quantum states. By proving a de Finetti representation for states subject to a sufficiently large class of constraints, we can derive all the desired results for a broad class of processes.

In this talk, I will introduce the main elements and ideas of the general boundary formulation [R. Oeckl. A local and operational framework for the foundations of physics. Advances in Theoretical and Mathematical Physics, 23(2):437–592, 2019. arXiv: 1610.09052.]. This is a formalism inspired by quantum gravity approaches and quantum information theoretic ideas and it generalises quantum field theory in such a way to deal with local measurements in local spacetime regions. It can therefore serve as a framework for reconciling quantum field theory with quantum information theory and describe measurement set-ups more general that the scattering (S-matrix) picture of particle physics. This is known to be non-trivial because the naïve application on quantum fields of mathematical objects representing measurements in the non-relativistic theory can lead to violations of locality and causality. This has been indicated by the Reeh-Schlieder theorem, as well as the more recent analysis by Sorkin [R. D. Sorkin. Impossible measurements on quantum fields. In B. L. Hu and T. A. Jacobson, editors, Directions in General Relativity: Papers in Honor of Dieter Brill, Volume 2, volume 2, page 293, January 1993.]. Here, I will focus on the composition of measurements (and observables) in relativistic quantum field theory and discuss how we deal with this problem in the context of the general boundary formulation.

I will introduce a protocol which allows to unitarily extract work out of sources of quantum states characterized only by a single type of coarse measurement. This defines a new notion of extractable work, which we call observational ergotropy, because it is directly related to observational entropy.

Wheeler’s delayed-choice experiment, a scenario wherein a classical apparatus, typically an interferometer, is settled only after the quantum system has entered it, has corroborated the complementarity principle. However, the quantum version of Wheeler’s delayed-choice experiment has challenged the robustness of this principle. Based on the visibility at the output of a quantum-controlled interferometer, a conceptual framework has been put forward which detaches the notions of wave and particle from the quantum state.
In this talk, I will present our results concerning a quantum-controlled reality experiment, a slightly modified setup that is based on exchanging the causal order between the two main operations of the quantum Wheeler’s delayed-choice arrangement. We employed an operational criterion of physical realism to reveal a different state of affairs concerning the wave-and-particle behavior in this new setup. An experimental proof-of-principle will be presented for a two-spin-1/2 system in an interferometric setup implemented in a nuclear magnetic resonance platform. Finally, it will be discussed how our results validate the complementarity principle.