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  • Journal article
    Barnard J, Lee J, Alexander O, Jarosch S, Garratt D, Picciuto R, Kowalczyk K, Ferchaud C, Gregory A, Matthews M, Marangos Jet al., 2022,

    Delivery of stable ultra-thin liquid sheets in vacuum for biochemical spectroscopy

    , Frontiers in Molecular Biosciences, ISSN: 2296-889X

    The development of ultra-thin flat liquid sheets capable of running in vacuum has provided an exciting new target for X-ray absorption spectroscopy in the liquid and solution phases. Several methods have become available for delivering in-vacuum sheet jets using different nozzle designs. We compare the sheets produced by two different types of nozzle; a commercially available borosillicate glass chip using microfluidic channels to deliver colliding jets, and an in-house fabricated fan spray nozzle which compresses the liquid on an axis out of a slit to achieve collision conditions. We find in our tests that both nozzles are suitable for use in X-ray absorption spectroscopy with the fan spray nozzle producing thicker but more stable jets than the commercial nozzle. We also provide practical details of how to run these nozzles in vacuum

  • Journal article
    Schwickert D, Ruberti M, Kolorenč P, Przystawik A, Skruszewicz S, Sumfleth M, Braune M, Bocklage L, Carretero L, Czwalinna MK, Diaman D, Düsterer S, Kuhlmann M, Palutke S, Röhlsberger R, Rönsch-Schulenburg J, Toleikis S, Usenko S, Viefhaus J, Vorobiov A, Martins M, Kip D, Averbukh V, Marangos JP, Laarmann Tet al., 2022,

    Charge-induced chemical dynamics in glycine probed with time-resolved Auger electron spectroscopy.

    , Struct Dyn, Vol: 9, ISSN: 2329-7778

    In the present contribution, we use x-rays to monitor charge-induced chemical dynamics in the photoionized amino acid glycine with femtosecond time resolution. The outgoing photoelectron leaves behind the cation in a coherent superposition of quantum mechanical eigenstates. Delayed x-ray pulses track the induced coherence through resonant x-ray absorption that induces Auger decay. Temporal modulation of the Auger electron signal correlated with specific ions is observed, which is governed by the initial electronic coherence and subsequent vibronic coupling to nuclear degrees of freedom. In the time-resolved x-ray absorption measurement, we monitor the time-frequency spectra of the resulting many-body quantum wave packets for a period of 175 fs along different reaction coordinates. Our experiment proves that by measuring specific fragments associated with the glycine dication as a function of the pump-probe delay, one can selectively probe electronic coherences at early times associated with a few distinguishable components of the broad electronic wave packet created initially by the pump pulse in the cation. The corresponding coherent superpositions formed by subsets of electronic eigenstates and evolving along parallel dynamical pathways show different phases and time periods in the range of ( - 0.3 ± 0.1 ) π ≤ ϕ ≤ ( 0.1 ± 0.2 ) π and 18.2 - 1.4 + 1.7 ≤ T ≤ 23.9 - 1.1 + 1.2 fs. Furthermore, for long delays, the data allow us to pinpoint the driving vibrational modes of chemical dynamics mediating charge-induced bond cleavage along different reaction coordinates.

  • Journal article
    Bellini M, Kwon H, Biagi N, Francesconi S, Zavatta A, Kim MSet al., 2022,

    Demonstrating quantum microscopic reversibility using coherent states of light

    , Physical Review Letters, Vol: 129, Pages: 1-6, ISSN: 0031-9007

    The principle of microscopic reversibility lies at the core of fluctuation theorems, which have extended our understanding of the second law of thermodynamics to the statistical level. In the quantum regime, however, this elementary principle should be amended as the system energy cannot be sharply determined at a given quantum phase space point. In this Letter, we propose and experimentally test a quantum generalization of the microscopic reversibility when a quantum system interacts with a heat bath through energy-preserving unitary dynamics. Quantum effects can be identified by noting that the backward process is less likely to happen in the existence of quantum coherence between the system’s energy eigenstates. The experimental demonstration has been realized by mixing coherent and thermal states in a beam splitter, followed by heterodyne detection in an optical setup. We verify that the quantum modification for the principle of microscopic reversibility is critical in the low-temperature limit, while the quantum-to-classical transition is observed as the temperature of the thermal field gets higher.

  • Journal article
    Tarrant J, Khokhlova M, Averbukh V, 2022,

    Publisher's Note: "Interferometry of quantum revivals" [J. Chem. Phys. 157, 054304 (2022)].

    , J Chem Phys, Vol: 157
  • Journal article
    Koukoulekidis N, Jee H, Jennings D, Kim M, Kwon Het al., 2022,

    Faster Born probability estimation via gate merging and frame optimisation

    , Quantum, Vol: 6, Pages: 838-838, ISSN: 2521-327X

    Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity present in the circuit frame representation quantifies the overhead on the number of samples required to achieve a certain precision. In this paper, we propose two classical sub-routines: circuit gate merging and frame optimisation, which optimise the circuit representation to reduce the sampling overhead. We show that the runtimes of both sub-routines scale polynomially in circuit size and gate depth. Our methods are applicable to general circuits, regardless of generating gate sets, qudit dimensions and the chosen frame representations for the circuit components. We numerically demonstrate that our methods provide improved scaling in the negativity overhead for all tested cases of random circuits with Clifford+T and Haar-random gates, and that the performance of our methods compares favourably with prior quasi-probability simulators as the number of non-Clifford gates increases.

  • Journal article
    Bressanini G, Kwon H, Kim MS, 2022,

    Noise thresholds for classical simulability of nonlinear boson sampling

    , PHYSICAL REVIEW A, Vol: 106, ISSN: 2469-9926
  • Journal article
    Zhang H, Wan L, Haug T, Mok W-K, Paesani S, Shi Y, Cai H, Chin LK, Karim MF, Xiao L, Luo X, Gao F, Dong B, Assad S, Kim MS, Laing A, Kwek LC, Liu AQet al., 2022,

    Resource-efficient high-dimensional subspace teleportation with a quantum autoencoder.

    , Sci Adv, Vol: 8

    Quantum autoencoders serve as efficient means for quantum data compression. Here, we propose and demonstrate their use to reduce resource costs for quantum teleportation of subspaces in high-dimensional systems. We use a quantum autoencoder in a compress-teleport-decompress manner and report the first demonstration with qutrits using an integrated photonic platform for future scalability. The key strategy is to compress the dimensionality of input states by erasing redundant information and recover the initial states after chip-to-chip teleportation. Unsupervised machine learning is applied to train the on-chip autoencoder, enabling the compression and teleportation of any state from a high-dimensional subspace. Unknown states are decompressed at a high fidelity (~0.971), obtaining a total teleportation fidelity of ~0.894. Subspace encodings hold great potential as they support enhanced noise robustness and increased coherence. Laying the groundwork for machine learning techniques in quantum systems, our scheme opens previously unidentified paths toward high-dimensional quantum computing and networking.

  • Journal article
    Song W, Lim Y, Jeong K, Lee J, Park JJ, Kim MS, Bang Jet al., 2022,

    Polynomial T-depth quantum solvability of noisy binary linear problem: from quantum-sample preparation to main computation

    , New Journal of Physics, Vol: 24, Pages: 1-11, ISSN: 1367-2630

    The noisy binary linear problem (NBLP) is known as a computationally hard problem, and therefore, it offers primitives for post-quantum cryptography. An efficient quantum NBLP algorithm that exhibits a polynomial quantum sample and time complexities has recently been proposed. However, the algorithm requires a large number of samples to be loaded in a highly entangled state and it is unclear whether such a precondition on the quantum speedup can be obtained efficiently. Here, we present a complete analysis of the quantum solvability of the NBLP by considering the entire algorithm process, namely from the preparation of the quantum sample to the main computation. By assuming that the algorithm runs on 'fault-tolerant' quantum circuitry, we introduce a reasonable measure of the computational time cost. The measure is defined in terms of the overall number of T gate layers, referred to as T-depth complexity. We show that the cost of solving the NBLP can be polynomial in the problem size, at the expense of an exponentially increasing logical qubits.

  • Journal article
    Zhang C, Tarbutt M, 2022,

    Quantum computation in a hybrid array of molecules and Rydberg atoms

    , PRX Quantum, Vol: 3, Pages: 1-17, ISSN: 2691-3399

    We show that an array of polar molecules interacting with Rydberg atoms is a promising hybrid system for scalable quantum computation. Quantum information is stored in long-lived hyperfine or rotational states of molecules which interact indirectly through resonant dipole-dipole interactions with Rydberg atoms. A two-qubit gate based on this interaction has a duration of 1 μs and an achievable fidelity of 99.9%. The gate has little sensitivity to the motional states of the particles – the molecules can be in thermal states, the atoms do not need to be trapped during Rydberg excitation, the gate does not heat the molecules, and heating of the atoms has a negligible effect. Within a large, static array, the gate can be applied to arbitrary pairs of molecules separated by tens of micrometres, making the scheme highly scalable. The molecule-atom interaction can also be used for rapid qubit initialization and efficient, non-destructive qubit readout, without driving any molecular transitions. Single qubit gates are driven using microwave pulses alone, exploiting the strong electric dipole transitions between rotational states. Thus, all operations required for large scale quantum computation can be done without moving the molecules or exciting them out of their ground electronic states.

  • Journal article
    Zhao H, Knolle J, Moessner R, Mintert Fet al., 2022,

    Suppression of Interband Heating for Random Driving

    , PHYSICAL REVIEW LETTERS, Vol: 129, ISSN: 0031-9007
  • Journal article
    Ferchaud C, Jarosch S, Avni T, Alexander O, Barnard J, Larsen E, Matthews M, Marangos Jet al., 2022,

    Interaction of an intense few-cycle infrared laser pulse with an ultrathin transparent liquid sheet

    , Optics Express, Vol: 30, Pages: 34684-34692, ISSN: 1094-4087

    We experimentally study the interaction between intense infrared few-cycle laser pulses and an ultrathin (∼2 µm) flat liquid sheet of isopropanol running in vacuum. We observe a rapid decline in transmission above a critical peak intensity of 50 TW/cm2 of the initially transparent liquid sheet, and the emission of a plume of material. We find both events are due to the creation of a surface plasma and are similar to processes observed in dielectric solids. After calculating the electron density for different laser peak intensities, we find an electron scattering rate of 0.3 fs-1 in liquid isopropanol to be consistent with our data. We study the dynamics of the plasma plume to find the expansion velocity of the plume front.

  • Journal article
    Völksen F, Devlin JA, Borchert MJ, Erlewein SR, Fleck M, Jäger JI, Latacz BM, Micke P, Nuschke P, Umbrazunas G, Wursten EJ, Abbass F, Bohman MA, Popper D, Wiesinger M, Will C, Blaum K, Matsuda Y, Mooser A, Ospelkaus C, Smorra C, Soter A, Quint W, Walz J, Yamazaki Y, Ulmer Set al., 2022,

    A high-Q superconducting toroidal medium frequency detection system with a capacitively adjustable frequency range >180 kHz.

    , Rev Sci Instrum, Vol: 93

    We describe a newly developed polytetrafluoroethylene/copper capacitor driven by a cryogenic piezoelectric slip-stick stage and demonstrate with the chosen layout cryogenic capacitance tuning of ≈60 pF at ≈10 pF background capacitance. Connected to a highly sensitive superconducting toroidal LC circuit, we demonstrate tuning of the resonant frequency between 345 and 685 kHz, at quality factors Q > 100 000. Connected to a cryogenic ultra low noise amplifier, a frequency tuning range between 520 and 710 kHz is reached, while quality factors Q > 86 000 are achieved. This new device can be used as a versatile image current detector in high-precision Penning-trap experiments or as an LC-circuit-based haloscope detector to search for the conversion of axion-like dark matter to radio-frequency photons. This new development increases the sensitive detection bandwidth of our axion haloscope by a factor of ≈1000.

  • Journal article
    Sempere Llagostera S, Patel RB, Walmsley IA, Kolthammer Wet al., 2022,

    Experimentally finding dense subgraphs using a time-bin encoded Gaussian boson sampling device

    , Physical Review X, ISSN: 2160-3308

    Gaussian boson sampling (GBS) is a quantum computing concept based on drawing samples from a multimode nonclassical Gaussian state using photon-number resolving detectors. It was initially posed as a near-term approach to achieve quantum advantage, and several applications have beenproposed since, including the calculation of graph features. For the first time, we use a time-bin encoded interferometer to implement GBS experimentally and extract samples to enhance the search for dense subgraphs in a graph. Our results indicate an improvement over classical methods for subgraphs of sizes three and four in a graph containing ten nodes. In addition, we numerically explore the role of imperfections in the optical circuit and on the performance of the algorithm.

  • Journal article
    Maimaris M, Pettipher AJ, Azzouzi M, Walke DJ, Zheng X, Gorodetsky A, Dong Y, Tuladhar Shakya P, Crespo H, Nelson J, Tisch J, Bakulin Aet al., 2022,

    Sub-10-fs observation of bound exciton formation in organic optoelectronic devices

    , Nature Communications, Vol: 13, ISSN: 2041-1723

    Fundamental mechanisms underlying exciton formation in organic semiconductors are complex and elusive as it occurs on ultrashort sub-100-fs timescales. Some fundamental aspects of this process, such as the evolution of exciton binding energy, have not been resolved in time experimentally. Here, we apply a combination of sub-10-fs Pump-Push-Photocurrent, Pump-Push-Photoluminescence, and Pump-Probe spectroscopies to polyfluorene devices to track the ultrafast formation of excitons. While Pump-Probe is sensitive to the total concentration of excited states, Pump-Push-Photocurrent and Pump-Push-Photoluminescence are sensitive to bound states only, providing access to exciton binding dynamics. We find that excitons created by near-absorption-edge photons are intrinsically bound states, or become such within 10 fs after excitation. Meanwhile, excitons with a modest >0.3 eV excess energy can dissociate spontaneously within 50 fs before acquiring bound character. These conclusions are supported by excited-state molecular dynamics simulations and a global kinetic model which quantitatively reproduce experimental data.

  • Journal article
    Tarrant J, Khokhlova M, Averbukh V, 2022,

    Interferometry of quantum revivals

    , JOURNAL OF CHEMICAL PHYSICS, Vol: 157, ISSN: 0021-9606
  • Journal article
    Ruberti M, Patchkovskii S, Averbukh V, 2022,

    Quantum coherence in molecular photoionization

    , PHYSICAL CHEMISTRY CHEMICAL PHYSICS, Vol: 24, Pages: 19673-19686, ISSN: 1463-9076
  • Journal article
    Sauvage F, Mintert F, 2022,

    Optimal Control of Families of Quantum Gates

    , PHYSICAL REVIEW LETTERS, Vol: 129, ISSN: 0031-9007
  • Journal article
    Frasinski LJ, 2022,

    Cumulant mapping as the basis of multi-dimensional spectrometry

    , PHYSICAL CHEMISTRY CHEMICAL PHYSICS, Vol: 24, Pages: 20776-20787, ISSN: 1463-9076
  • Journal article
    Ma Y, Pace MCC, Kim MS, 2022,

    Unifying the sorensen-molmer gate and the milburn gate with an optomechanical example

    , Physical Review A: Atomic, Molecular and Optical Physics, Vol: 106, ISSN: 1050-2947

    The Sørensen-Mølmer gate and Milburn gate are two geometric phase gates, generating nonlinear self-interaction of a target mode via its interaction with an auxiliary mechanical mode, in the continuous- and pulsed-interaction regimes, respectively. In this paper we aim at unifying the two gates by demonstrating that the Sørensen-Mølmer gate is the continuous limit of the Milburn gate, emphasizing the geometrical interpretation in the mechanical phase space. We explicitly consider imperfect gate parameters, focusing on relative errors in time for the Sørensen-Mølmer gate and in phase angle increment for the Milburn gate. We find that, although the purities of the final states increase for the two gates upon reducing the interaction strength together with traversing the mechanical phase space multiple times, the fidelities behave differently. We point out that the difference exists because the interaction strength depends on the relative error when taking the continuous limit from the pulsed regime, thereby unifying the mathematical framework of the two gates. We demonstrate this unification in the example of an optomechanical system, where mechanical dissipation is also considered. We highlight that the unified framework facilitates our method of deriving the dynamics of the continuous-interaction regime without solving differential equations.

  • Journal article
    Kanari-Naish LA, Clarke J, Qvarfort S, Vanner MRet al., 2022,

    Two-mode Schrodinger-cat states with nonlinear optomechanics: generation and verification of non-Gaussian mechanical entanglement

  • Journal article
    Danilov D, Tran T, Bearpark MJ, Marangos JP, Worth GA, Robb MAet al., 2022,

    How electronic superpositions drive nuclear motion following the creation of a localized hole in the glycine radical cation.

    , J Chem Phys, Vol: 156

    In this work, we have studied the nuclear and electron dynamics in the glycine cation starting from localized hole states using the quantum Ehrenfest method. The nuclear dynamics is controlled both by the initial gradient and by the instantaneous gradient that results from the oscillatory electron dynamics (charge migration). We have used the Fourier transform (FT) of the spin densities to identify the "normal modes" of the electron dynamics. We observe an isomorphic relationship between the electron dynamics normal modes and the nuclear dynamics, seen in the vibrational normal modes. The FT spectra obtained this way show bands that are characteristic of the energy differences between the adiabatic hole states. These bands contain individual peaks that are in one-to-one correspondence with atom pair (+·) ↔ (·+) resonances, which, in turn, stimulate nuclear motion involving the atom pair. With such understanding, we anticipate "designer" coherent superpositions that can drive nuclear motion in a particular direction.

  • Journal article
    Garratt D, Misiekis L, Wood D, Larsen E, Matthews M, Alexander O, Ye P, Jarosch S, Ferchaud C, Struber C, Johnson A, Bakulin A, Penfold T, Marangos Jet al., 2022,

    Direct observation of ultrafast exciton localization in an organic semiconductor with soft X-ray transient absorption spectroscopy

    , Nature Communications, Vol: 13, ISSN: 2041-1723

    The localization dynamics of excitons in organic semiconductors influence the efficiency of charge transfer and separation in these materials. Here we apply time-resolved X-ray absorption spectroscopy to track photoinduced dynamics of a paradigmatic crystalline conjugated polymer: poly(3-hexylthiophene) (P3HT) commonly used in solar cell devices. The π→π* transition, the first step of solar energy conversion, is pumped with a 15 fs optical pulse and the dynamics are probed by an attosecond soft X-ray pulse at the carbon K-edge. We observe X-ray spectroscopic signatures of the initially hot excitonic state, indicating that it is delocalized over multiple polymer chains. This undergoes a rapid evolution on a sub 50 fs timescale which can be directly associated with cooling and localization to form either a localized exciton or polaron pair.

  • Journal article
    Zhao H, Mintert F, Knolle J, Moessner Ret al., 2022,

    Localization persisting under aperiodic driving

    , PHYSICAL REVIEW B, Vol: 105, ISSN: 2469-9950
  • Journal article
    Schwickert D, Ruberti M, Kolorenc P, Usenko S, Przystawik A, Baev K, Baev I, Braune M, Bocklage L, Czwalinna MK, Deinert S, Duesterer S, Hans A, Hartmann G, Haunhorst C, Kuhlmann M, Palutke S, Roehlsberger R, Roensch-Schulenburg J, Schmidt P, Toleikis S, Viefhaus J, Martins M, Knie A, Kip D, Averbukh V, Marangos JP, Laarmann Tet al., 2022,

    Electronic quantum coherence in glycine molecules probed with ultrashort x-ray pulses in real time

    , SCIENCE ADVANCES, Vol: 8, ISSN: 2375-2548
  • Journal article
    Cao N, Xie J, Zhang A, Hou S-Y, Zhang L, Zeng Bet al., 2022,

    Neural networks for quantum inverse problems

    , New Journal of Physics, Vol: 24, Pages: 063002-063002

    <jats:title>Abstract</jats:title> <jats:p>Quantum inverse problem (QIP) is the problem of estimating an unknown quantum system from a set of measurements, whereas the classical counterpart is the inverse problem of estimating a distribution from a set of observations. In this paper, we present a neural-network-based method for QIPs, which has been widely explored for its classical counterpart. The proposed method utilizes the quantumness of the QIPs and takes advantage of the computational power of neural networks to achieve remarkable efficiency for the quantum state estimation. We test the method on the problem of maximum entropy estimation of an unknown state <jats:italic>ρ</jats:italic> from partial information both numerically and experimentally. Our method yields high fidelity, efficiency and robustness for both numerical experiments and quantum optical experiments.</jats:p>

  • Journal article
    Chevalier H, Kwon H, Khosla KE, Pikovski I, Kim MSet al., 2022,

    Many-body probes for quantum features of spacetime

    , AVS Quantum Science, Vol: 4, Pages: 1-10, ISSN: 2639-0213

    Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work, we inspect the capacity for correlated many-body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we work out the full Magnus expansion. We numerically show that it is possible to have superquadratic scaling of a nonstandard phase term, arising from the modification to the commutation relations, with coupled mechanical oscillators.

  • Working paper
    Sun B, Morozko F, Salter PS, Moser S, Pong Z, Patel RB, Walmsley IA, Hazan A, Barré N, Jesacher A, Fells J, Katiyi A, Novitsky A, Karabchevsky A, Booth MJet al., 2022,

    On-chip beam rotators, polarizers and adiabatic mode converters through low-loss waveguides with variable cross-sections

    , Publisher: ArXiv

    Photonics integrated circuitry would benefit considerably from the ability toarbitrarily control waveguide cross-sections with high precision and low loss,in order to provide more degrees of freedom in manipulating propagating light.Here, we report on a new optical-fibres-compatible glass waveguide byfemtosecond laser writing, namely spherical phase induced multi-core waveguide(SPIM-WG), which addresses this challenging task with three dimensional on-chiplight control. Precise deformation of cross-sections is achievable along thewaveguide, with shapes and sizes finely controllable of high resolution in bothhorizontal and vertical transversal directions. We observed that thesewaveguides have high refractive index contrast of 0.017, low propagation lossof 0.14 dB/cm, and very low coupling loss of 0.19 dB coupled from a single modefibre. SPIM-WG devices were easily fabricated that were able to perform on-chipbeam rotation through varying angles, or manipulate polarization state ofpropagating light for target wavelengths. We also demonstrated SPIM-WG modeconverters that provide arbitrary adiabatic mode conversion with highefficiency between symmetric and asymmetric non-uniform modes; examples includecircular, elliptical modes and asymmetric modes from ppKTP waveguides which aregenerally applied in frequency conversion and quantum light sources. Createdinside optical glass, these waveguides and devices have the capability tooperate across ultra-broad bands from visible to infrared wavelengths. Thecompatibility with optical fibre also paves the way toward packaged photonicintegrated circuitry, which usually needs input and output fibre connections.

  • Working paper
    Sempere-Llagostera S, Patel RB, Walmsley IA, Kolthammer WSet al., 2022,

    Experimentally finding dense subgraphs using a time-bin encoded Gaussian boson sampling device

    , Publisher: Arxiv

    Gaussian Boson Sampling (GBS) is a quantum computing concept based on drawingsamples from a multimode nonclassical Gaussian state using photon-numberresolving detectors. It was initially posed as a near-term approach aiming toachieve quantum advantage, but several applications have been proposed eversince, such as the calculation of graph features or molecular vibronic spectra,among others. For the first time, we use a time-bin encoded interferometer toimplement GBS experimentally and extract samples to enhance the search fordense subgraphs in a graph. Our results indicate an improvement over classicalmethods for subgraphs of sizes three and four in a graph containing ten nodes.In addition, we numerically explore the role of imperfections in the opticalcircuit and on the performance of the algorithm.

  • Journal article
    Joseph D, Martinez AJ, Ling C, Mintert Fet al., 2022,

    Quantum mean-value approximator for hard integer-value problems

    , PHYSICAL REVIEW A, Vol: 105, ISSN: 2469-9926
  • Journal article
    Alexander R, Gvirtz-Chen S, Jennings D, 2022,

    Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system

    , New Journal of Physics, Vol: 24, ISSN: 1367-2630

    Symmetry principles are fundamental in physics, and while they are well understood within Lagrangian mechanics, their impact on quantum channels has a range of open questions. The theory of asymmetry grew out of information-theoretic work on entanglement and quantum reference frames, and allows us to quantify the degree to which a quantum system encodes coordinates of a symmetry group. Recently, a complete set of entropic conditions was found for asymmetry in terms of correlations relative to infinitely many quantum reference frames. However, these conditions are difficult to use in practice and their physical implications unclear. In the present theoretical work, we show that this set of conditions has extensive redundancy, and one can restrict to reference frames forming any closed surface in the state space that has the maximally mixed state in its interior. This in turn implies that asymmetry can be reduced to just a single entropic condition evaluated at the maximally mixed state. Contrary to intuition, this shows that we do not need macroscopic, classical reference frames to determine the asymmetry properties of a quantum system, but instead infinitesimally small frames suffice. Building on this analysis, we provide simple, closed conditions to estimate the minimal depolarization needed to make a given quantum state accessible under channels covariant with any given symmetry group.

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