Abstract
We treat the Cooper pairs in the superconducting electrodes of a Josephson junction (JJ) as an open system, coupled via Andreev scattering to external baths of electrons. The disequilibrium between the baths generates the direct-current bias applied to the JJ. In the weak-coupling limit we obtain a Markovian master equation that provides a simple dynamical description consistent with the main features of the JJ, including the form of the current-voltage characteristic, its hysteresis, and the appearance under periodic voltage driving of discrete Shapiro steps. For small dissipation, our model also exhibits a self-oscillation of the JJ’s electrical dipole around mean voltage V. This self-oscillation, associated with “hidden attractors” of the nonlinear equations of motion, explains the observed production of monochromatic radiation.
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.
Bounding the set of local operations from their classical action
Date: Monday, November 13, 2023
Time: 14:15
Host: Quantum Chaos and Quantum Information (Jagiellonian University)
Passcode: please contact albertrico23 at gmail.com
Speaker: Albert Rico (UJ)
Abstract
Bell inequalities’s journey from rags to riches of quantum
theory was a long one. Proposed by John Bell in 1964, the inequalities
were designed to check whether quantum theory, with its inherent
statistical predictions, is a complete description of physical reality
or whether it is just a provisional construct, with an underlying
hidden structure which, once discovered, would offer precise
predictions. The subsequent pioneering experiments of outliers, such
as John Clauser (1972) and Alain Aspect (1982), showed that Bell’s
inequalities can be violated. However, these experiments were barely
noticed at that time. Quantum theory is admittedly strange, but it
worked and the research community just carried on using it in an
instrumental way, making successful statistical predictions while
avoiding anything related to their interpretations. Bell inequalities
were viewed as a philosophical topic with no practical value and hence
not worthy of the attention of serious scientists. When Bell
inequalities snagged my imagination, I was just a PhD student with
nothing to lose. In 1991, I reformulated Bell inequalities as the test
for eavesdropping in cryptography, paving the way for the most secure
communication systems to date, known as the device independent quantum
key distribution. The new narrative around Bell inequalities created
an additional motivation to close all possible loopholes in the
previous experiments. In the new context it seemed reasonable. Nature
would have to be very malicious if it were to cheat selectively; on
locality in some experiments and exploring detection loopholes in some
others. In contrast, an eavesdropper has all the rights to be
malicious. Closing the loopholes posed an experimental challenge but
gradually, due to the efforts of several experimental groups, to
mention only those of Anton Zeilinger (2015), the loopholes were
closed and device independent cryptography became a realistic
experimental proposition. Cryptography offered a lifeline to quantum
foundations and in return the experimental tools developed to pursue
esoteric philosophical questions gave cryptography unprecedented
security. The curiosity and perseverance of the few brave souls who
made this happen (and who are still alive) were finally rewarded with
the 2022 Nobel Prize in Physics.
Constant-sized self-tests for maximally entangled states and single projective measurements
Date: Wednesday, October 25, 2023
Time: 14:30
Host: Quantum Information and Quantum Computing Working Group
Speaker: Jurij Volčič (Drexel University, United States)
Abstract
Self-testing is a powerful certification of quantum systems relying on measured, classical statistics. This talk considers self-testing in bipartite Bell scenarios with small number of inputs and outputs, but with quantum states and measurements of arbitrarily large dimension. Firstly, it is shown that every maximally entangled state can be self-tested with four binary measurements per party. This result extends the earlier work of Fu (2022) on maximally entangled states of infinitely many even dimensions, and Mančinska-Prakash-Schafhauser (2021) on maximally entangled states of all odd dimensions. Secondly, it is shown that every single binary projective measurement can be self-tested with five binary measurements per party. A similar statement holds for self-testing of projective measurements with more than two outputs. These results are enabled by the representation theory of tuples of projections that add to a scalar multiple of the identity. Structure of their irreducible representations, analysis of their spectral features and post-hoc self-testing are the primary methods for constructing these self-tests with small number of inputs and outputs.
Unbounded device-independent quantum key rates from arbitrarily small non-locality
Abstract
Device-independent quantum key distribution allows for proving the security of a shared cryptographic key between two distant parties with potentially untrusted devices. The security proof is based on the measurement outcome statistics (correlation) of a Bell experiment, and security is guaranteed by the laws of quantum theory. While it is known that the observed correlation must be Bell non-local in order to prove security, recent results show that Bell non-locality is in general not sufficient for standard device-independent quantum key distribution. In this work, we show that conversely, there is no lower bound on the amount of non-locality that is sufficient for device-independent quantum key distribution. Even more so, we show that from certain correlations that exhibit arbitrarily small non-locality, one can still extract unbounded device-independent key rates. Therefore, a quantitative relation between device-independent key rates and Bell non-locality cannot be drawn in general. Our main technique comprises a rigorous connection between self-testing and device-independent quantum key distribution, applied to a recently discovered family of Bell inequalities with arbitrarily many measurement outcomes.
Pretty good simulation of all quantum measurements by projective measurements in finite-dimensional quantum systems
Speaker: Michał Oszmaniec (Center for Theoretical Physics PAS/ NASK)
Abstract
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.
Abstract
In most realistic situations a quantum system is never perfectly isolated and has to be considered as an open quantum system: it is coupled to an environment that induces decoherence and dissipation. These phenomena can not be described within the standard Schroedinger unitary evolution. In my talk I provide a basic introduction to Markovian semigroups stressing the very concept of complete positivity which plays a key role in modern quantum information theory being a mathematical representation of a quantum channel. However, quantum systems cannot always be described within a Markovian semigroup, which requires a large separation of system and environment time scales. I discuss basic concepts of non-Markovian evolution which are illustrated with simple physical models. Finally, I discuss a natural connection to quantum stochastic processes and the property of Markovianity and classicality.
Objectivity of observables in GPTs and exploring non-locally tomographic theories
Speaker: Roberto Baldijão (ICTQT – Univerisity of Gdańsk)
Abstract
In this talk, I will present two project ideas I think will be nice to work on. The first idea is to analyze Objectivity of Observables in the framework of generalized probabilistic theories (GPTs). Objectivity of Observables was first proven by Brandão, Piani and Horodecki for quantum theory; it states that after a system S interacts with many other systems (for any interaction), the information about S stored in these other systems is typically represented by one observable acting on S. This was a huge step for the quantum Darwinism program, as an explanation for the emergence of a classical world.
The second idea is to explore features of non-locally tomographic GPTs. In these kinds of theories, processes cannot be determined when probed by local processes — one must always have access to some global degrees of freedom to fully characterize a process. In the talk, I will use entanglement and monogamy of entanglement in these theories to exemplify why I think there is much there to explore. Finally, if there is some time, I can explain intuitively how these two projects might be connected. The spirit of the talk is mainly to describe these ideas and collaborate with whomever would like to work on them. So, if you like any of these problems, please join me in these attempts 😀
Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario
Date: Wednesday, September 27, 2023
Time: 14:30
Host: Quantum Information and Quantum Computing Working Group, Meeting ID: 844 2780 6931
Speaker: Gábor Drótos (Atomki, Debrecen, Hungarian Academy of Sciences)
Abstract
Self-testing is a powerful method for certifying quantum systems. Initially proposed in the device-independent (DI) setting, self-testing has since been relaxed to the semi-device-independent (semi-DI) setting. We focus on the self-testing of a specific type of non-projective qubit measurements belonging to a one-parameter family, using the semi-DI prepare-and-measure (PM) scenario. Remarkably, we identify the simplest PM scenario discovered so far, involving only four preparations and four measurements, for self-testing the fourth measurement. This particular measurement is a four-outcome non-projective positive operator-valued measure (POVM) and falls in the class of semisymmetric informationally complete (semi-SIC) POVMs introduced by Geng et al. [Phys. Rev. Lett. 126, 100401 (2021)]. To achieve this, we develop analytical techniques for semi-DI self-testing in the PM scenario.
Certification of Entanglement Using Quantum Steering in Networks
Date: Wednesday, September 20, 2023
Time: 14:30
Host: Quantum Information and Quantum Computing Working Group, Meeting ID: 844 2780 6931
Abstract
Bipartite low dimensional entanglement has been studied extensively. However, many findings cannot be extrapolated to multiple parties and moreover, increasing the dimensions of the systems adds complexity to the entanglement structure. We are interested in characterising the degree of high-dimensional entanglement, specifically focusing on various multipartite quantum steering scenarios. One such example is a triangle network with only one trusted party, or more generally a line network with some trusted parties. We investigate what can be deduced about the strength of entanglement between the different nodes of the network in such scenarios. We are especially interested in entanglement dimensionality, i.e. the question of how many degrees of freedom can be certified to be entangled, for which we provide analytical bounds.
Analyzing quantum entanglement with the Schmidt decomposition in operator space
Date: Wednesday, July 12, 2023
Time: 14:30
Host: Quantum Information and Quantum Computing Working Group, Meeting ID: 844 2780 6931
Abstract
Verifying entanglement between parties is essential for creating a secure quantum network, and Bell tests are the most rigorous method for doing so. However, if there is any signalling between the parties, then the violation of these inequalities can no longer be used to draw conclusions about the presence of entanglement. There is a pressing need to examine the role of signalling in quantum communication protocols from multiple perspectives, including communication security, physics foundations, and resource utilization while also promoting innovative technological applications. Here, we propose a semi-device independent protocol that allows us to numerically correct for effects of correlations in experimental probability distributions, caused by statistical fluctuations and experimental imperfections. Our noise robust protocol presents a relaxation of a tomography-based optimisation method called the steering robustness. The proposed protocol is numerically and experimentally analyzed in the context of random, misaligned measurements, correcting for signalling where necessary, resulting in a higher probability of violation compared to existing state-of-the-art inequalities. Our work demonstrates the power of semidefinite programming for entanglement verification and brings quantum networks closer to practical applications.
