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Entanglement Disparity: Teleportation Asymmetry in Bipartite Non-Abelian Anyonic Systems
Manabendra Nath BeraICTS:30939 -
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Counterfactual Quantum trajectories: Given that my photo detector clicked, what would have happened with a different type of a detector?
Ingita BICTS:31128Quantum trajectory theory, also known as quantum state filtering, enables us to estimate the state of a quantum system conditioned on the measurement we perform. In cases where we measure the fluorescence from a driven two-level atom with an inefficient photo detector, the conditioned state of the atom is generally not pure, except immediately after a photon detection since then we know that the atom is in the ground state. For the detection schemes such as homodyne measurement the state is never pure since it gives rise to quantum state diffusion and not quantum state jumps. In these scenarios questions can be asked as:
Given that I did use a photo detector and did see a particular time sequence of detections, how would the atom have behaved if instead I had chosen to measure the fluorescence using a homodyne detection scheme?
These questions are called counterfactual questions. Counterfactuality has played significant roles and has a long history in philosophy of trying to make sense of such questions. There are various approaches in how to evaluate such counterfactual questions. One such influential and attractive approach is that of David Lewis where he has a generalized analysis for counterfactuals.Analysis 2. A counterfactual " If it were that A, then it would be that C" is (non-vacuously) true if and only if some (accessible) world where both A and C are true is more similar to our actual world, overall, than is any world where A is true, but C is false.
To evaluate our atom counterfactual problem we use his approach under the two main considerations:
1) To avoid any big, widespread, diverse violations of law.
The antecedent of our counterfactual ( the thing that we propose to change) is our choice of measurement and that is within the laws of Quantum theory.
2) Maximize the spatiotemporal region throughout which perfect match of particular fact prevails.
Thus, in evaluating the counterfactual problem, any information not collected by the primary detector can be modeled as photon absorptions and should be held fixed, under the above consideration.
Denoting these other 'clicks' , described by some list of times M, and using the actual observed record of photon-counts denoted by the list of times, N, we can calculate a conditional probability of M given N. Following this we evaluate a second conditional probability with which we are most likely to observe a homodyne record over time ,Y , if we were ( counterfactually) making a homodyne measurement given M ( since M remains fixed). Conditioning the actual state (the state conditioned on all the measurements in the counterfactual case) of the atom on these probabilities and performing an ensemble average over all possible M and Y would give us the best ( relative to trace-mean-square-deviation cost function) estimate of the counterfactual state which answers the question.
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Optimal speed of quantum operations in open quantum systems
Sarfraj FencyICTS:31127Achieving high-fidelity and fast quantum state manipulation under realistic dissipation conditions remains a pivotal challenge in quantum computing and quantum information processing. Real-world quantum systems face dual sources of dissipation: environmental noise and drive-induced effects, which are often overlooked in existing control protocols. These limitations hinder the practical implementation of high-speed, accurate quantum operations.
In this work, we propose a method for designing pulse profiles that drive a quantum system from an initial state to a target state with both high fidelity and minimal time. Leveraging the GRAPE algorithm, our approach explicitly accounts for both environmental and drive-induced dissipation, ensuring robust performance across diverse quantum platforms.
Our findings highlight two critical insights: (1) the existence of an optimal evolution time that maximizes fidelity and (2) the counterintuitive enhancement of fidelity at lower drive strengths. These results pave the way for robust quantum control in open systems, addressing key obstacles to scaling quantum technologies. By improving the efficiency and accuracy of quantum operations, our method contributes to the realization of practical quantum computers and advanced quantum sensing technologies, even in the presence of realistic dissipation.
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Doppler-Enhanced Quantum Magnetometry with Rydberg atoms
Sanjukta RoyICTS:30934Rydberg atoms are giant atoms with the outer electron in a highly excited state with large values of the principal quantum number n. Rydberg atoms are highly sensitive to external fields, imparting these atoms extraordinary characteristics for Quantum sensing of electromagnetic fields.
In this talk, I will describe our recent results on Doppler-enhanced Quantum magnetometry with Rydberg atoms. We demonstrate in this work that one can harness Doppler shifts in an unconventional configuration of laser beams for Rydberg excitation to produce an order-of-magnitude enhanced response to a magnetic field as compared to the commonly used conventional configuration. We explain and generalize our findings with theoretical modelling and simulations based on a Lindblad master equation.
I will also discuss our recent observations on the effect of interatomic interaction in Autler-Townes splitting in ultra-cold Rydberg atoms. Our measurements on highly excited Rydberg atoms are directed towards Quantum sensing, Quantum computing and Quantum simulation of many-body physics with individual Rydberg atoms in an array of optical tweezers. -
Quantum Thermodynamics and non-Markovian physics
Subhashish BanerjeeICTS:30938After motivating the need for a study of Open Quantum Systems, I introduce, briefly, some recent developments in the efforts to understand non-Markovian phenomenon.
The discussion about non-Markovian behaviour is made in the backdrop of the Garraway model. This is followed by an introduction to notions such as ergotropy, entropy production, power, in the context of quantum thermodynamics.
Two types of Quantum Thermodynamic devices: Quantum Battery and Quantum Heat Engine are discussed.
These are then illustrated on open system models; (a). the Garraway type, (b). central spin model, (c). Quantum Brownian Motion, (d). two-qubit decoherence. -
Asymptotic behavior and feedback stabilization of quantum trajectories (L7)
Nina AminiICTS:30937In this lecture, we provide an introduction to quantum trajectory theory. We present various mathematical problems that arise within this context. In particular, we introduce approaches for analyzing the asymptotic behavior, convergence speed, and stabilization of quantum trajectories toward different states or subspaces through feedback control strategies. Our study includes both quantum non-demolition (QND) measurements and generic (non-QND) measurements in discrete-time and continuous-time settings.
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Detecting PPT entanglement in Symmetric Quantum States
Aabhas GulatiICTS:31120We introduce and study bipartite quantum states that are invariant under the local action of the cyclic sign group. Due to symmetry, these states are sparse and can be parameterized by a triple of vectors. Their important semi-definite properties, such as positivity and positivity under partial transpose (PPT), can be simply characterized in terms of these vectors and their discrete Fourier transforms. We study in detail the entanglement properties of this family of symmetric states, showing in particular that it contains PPT entangled states. For states that are diagonal in the Dicke basis, deciding separability is equivalent to a circulant version of the complete positivity problem. We provide some geometric results for the PPT cone, showing in particular that it is polyhedral. In local dimension less than 5, we completely characterize these sets and construct entanglement witnesses; some partial results are also obtained for d = 6, 7. Finally, we present some novel graph-theoretic techniques to detect entanglement in quantum states with symmetry, and construction of various families of PPT entangled states in all dimensions.
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Time-resolved Stochastic Dynamics of Quantum Thermal Machines
Abhaya HegdeICTS:31119Steady-state quantum thermal machines are typically characterized by a continuous flow of heat between different reservoirs. However, at the level of discrete stochastic realizations, heat flow is unraveled as a series of abrupt quantum jumps, each representing an exchange of finite quanta with the environment. In this work, we present a framework that resolves the dynamics of quantum thermal machines into cycles classified as engine-like, cooling-like, or idle. We analyze the statistics of individual cycle types and their durations, enabling us to determine both the fraction of cycles useful for thermodynamic tasks and the average waiting time between cycles of a given type. Central to our analysis is the notion of intermittency, which captures the operational consistency of the machine by assessing the frequency and distribution of idle cycles. Our framework offers a novel approach to characterizing thermal machines, with significant relevance to experiments involving mesoscopic transport through quantum dots.
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Quantum Alternating Operator Ansatz for the Preparation and Detection of Long-Lived Singlet States in NMR
Vishal VarmaICTS:31122Designing efficient and robust quantum control strategies is vital for developing quantum technologies. One recent strategy is the Quantum Alternating Operator Ansatz (QAOA) sequence that alternatively propagates under two noncommuting Hamiltonians, whose control parameters can be optimized to generate a gate or prepare a state. Here, we describe the design of a QAOA sequence to prepare long-lived singlet states (LLS) from the thermal state in NMR. With extraordinarily long lifetimes exceeding the spin-lattice relaxation time constant $T_1$, LLS have been of great interest for various applications, from spectroscopy to medical imaging. Accordingly, designing sequences for efficiently preparing LLS in a general spin system is crucial. Using numerical analysis, we study the efficiency and robustness of our QAOA sequence over a wide range of errors in the control parameters. Using a two-qubit NMR register, we conduct an experimental study to benchmark our QAOA sequence against other prominent methods of LLS preparation and observe superior performance, especially under noisy conditions.
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Josephson-Current Signatures of Unpaired Floquet Majorana Bound States
Rekha KumariICTS:31121We theoretically study the transport signatures of unpaired Floquet Majorana bound states in the Josephson current of weakly linked, periodically driven topological superconductors. We obtain the occupation of the Floquet Majorana modes in the presence of weak coupling to thermal leads analytically, and show that, similar to static superconductors, the Josephson current involving Floquet Majorana bound states is also 4π-periodic in the phase difference across the junction, and also depends linearly on the coupling between superconductors. Moreover, unlike the static case, the amplitude of the Josephson current can be tuned by setting the unbiased chemical potential of the driven superconductors at multiple harmonics of the drive frequency. As a result, we uncover a Josephson Floquet sum rule for driven superconductors. We confirm our analytical expressions for Josephson current, the occupation of Floquet bands, and a perturbative analysis of the quasienergies with numerically exact results.
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The Influence of Noise and Monitoring On Symmetry Breaking and Chaos
Adolfo del CampoICTS:30935In this talk, we study how noise and quantum monitoring shape symmetry breaking and chaos. We discuss the simulation of complex open quantum systems using classical noise and how noise limits adiabatic strategies, giving rise to anti-Kibble-Zurek scaling. We further show how spontaneous symmetry breaking is modified in the presence of an observer whose action is described by continuous quantum measurements. In the second part of the talk, we show how the signatures of Hamiltonian quantum chaos in the spectral form factor are suppressed energy dephasing while they are enhanced when the dynamics is conditioned to the absence of con quantum jumps.
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Entanglement Disparity: Teleportation Asymmetry in Bipartite Non-Abelian Anyonic Systems
Manabendra Nath BeraICTS:30939Non-Abelian anyons, a promising platform for fault-tolerant topological quantum computation, adhere to the charge super-selection rule (cSSR), which imposes restrictions on physically allowed states and operations. However, the ramifications of cSSR and fusion rules in anyonic quantum information theory remain largely unexplored. In this talk, we unveil that the information-theoretic characteristics of anyons diverge fundamentally from those of non-anyonic systems such as qudits, bosons, and fermions and display intricate structures. In bipartite anyonic systems, pure states may have different marginal spectra, and mixed states may contain pure marginal states. More striking is that in a bipartite pure entangled state, parties may lack equal access to entanglement. This we call entanglement disparity, and it is manifested in asymmetric quantum teleportation employing an entangled anyonic state shared between Alice and Bob, where Alice can perfectly teleport unknown quantum information to Bob, but Bob lacks this capability. These traits challenge conventional understanding, necessitating new approaches to characterize quantum information and correlations in anyons. We expect that these distinctive features will also be present in non-Abelian lattice gauge field theories. Our findings significantly advance the understanding of the information-theoretic aspects of anyons and may lead to realizations of quantum communication and cryptographic protocols where one party holds sway over the other.
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Asymptotic behavior and feedback stabilization of quantum trajectories (L7)
Nina AminiICTS:30933In this lecture, we provide an introduction to quantum trajectory theory. We present various mathematical problems that arise within this context. In particular, we introduce approaches for analyzing the asymptotic behavior, convergence speed, and stabilization of quantum trajectories toward different states or subspaces through feedback control strategies. Our study includes both quantum non-demolition (QND) measurements and generic (non-QND) measurements in discrete-time and continuous-time settings.