# Weekly Papers on Quantum Foundations (31)

Time-energy uncertainty relation for noisy quantum metrology. (arXiv:2207.13707v1 [quant-ph])

Detection of weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. We consider a quantum system initialized in a pure state and whose evolution is goverened by a Hamiltonian $H$; a measurement can later estimate the time $t$ for which the system has evolved. In this work, we introduce and study a fundamental trade-off which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. Specifically, we consider an idealized scenario in which Alice prepares an initial pure state of the clock, allows the clock to evolve for a time $t$ that is not precisely known, and then transmits the clock through a noisy channel to Bob. The environment (Eve) receives any information that is lost. We prove that Bob’s loss of quantum Fisher information (QFI) about $t$ is equal to Eve’s gain of QFI about a complementary energy parameter. We also prove a more general trade-off that applies when Bob and Eve wish to estimate the values of parameters associated with two non-commuting observables. We derive the necessary and sufficient conditions for the accuracy of the clock to be unaffected by the noise. These are a subset of the Knill-Laflamme error-correction conditions; states satisfying these conditions are said to form a metrological code. We provide a scheme to construct metrological codes in the stabilizer formalism. We show that there are metrological codes that cannot be written as a quantum error-correcting code with similar distance in which the Hamiltonian acts as a logical operator, potentially offering new schemes for constructing states that do not lose any sensitivity upon application of a noisy channel. We discuss applications of our results to sensing using a many-body state subject to erasure or amplitude-damping noise.

Post-selection and quantum energetics. (arXiv:2207.14194v1 [quant-ph])

We investigate the anomalous energy change of the measurement apparatus when a qubit is measured in bases that do not commute with energy. We model two possible measurement implementations: one is a quantum clock model with a completely time-independent Hamiltonian, while the other is a Jaynes-Cummings model which is time-dependent but conserves the total excitation number. We look at the mean energy change of the measurement apparatus in both models, conditioned on the qubit post-selection, and find that this change can be much greater than the level spacing of the qubit, like an anomalous weak value. In the clock model, the expression for the apparatus energy shift explicitly contains the weak value of the qubit Hamiltonian. However, in our case, no explicit weak measurements are carried out. Our two models give different results, which we explain to be a consequence of the non-degenerate spectrum of the Jaynes-Cummings model. We compare our calculations in the Jaynes-Cummings model with the experimental data of [J. Stevens, et al, arXiv:2109.09648 (2021)] and find good agreement when the conditions of our derivation are valid.

Black Hole as a Bound State of Semi-classical Degrees of Freedom. (arXiv:2207.14274v1 [hep-th])

A black hole is considered as a bound state of semi-classical degrees of freedom with maximum gravity. For a configuration of those responsible for the area entropy, the information distribution determines the interior metric through the semi-classical Einstein equation. Then, the bound state has no horizon or singularity, and the interior is a continuous stacking of $AdS_2\times S^2$ with a $AdS$ radius close to the Planck length and behaves like a thermal state at a near-Planckian local temperature. Integrating the entropy density over the interior volume reproduces the area law exactly. This indicates that the dynamics of gravity plays an essential role in the change of entropy from the volume law to the area law.

On the Free Will Theorem. (arXiv:2207.06295v2 [quant-ph] UPDATED)

We strengthen the Free Will Theorem, which proved the spontaneity of particles, based on the free will of the experimenter. The new result is unconditional, and does not require the experimenter’s free will to prove the particles’ spontaneity.

Time, space and matter in the primordial universe. (arXiv:2207.13722v1 [physics.hist-ph])

Authors: Francesca Vidotto

Time, space, and matter are categories of our reasoning, whose properties appear to be fundamental. However, these require a scrutiny as in the extreme regime of the primordial universe these present quantum properties. What does it mean for time to be quantum? What does it mean for space? Are space and time disappearing, or what is disappearing are simply the categories we have been using to understand them? Concepts such as the superposition of causal structures or the quantum granularity of space require our attention and should be clarified to understand the physics of the primordial universe. The novelty that this brings requires us to reflect on matter as well: How can matter be defined on a granular space? Is quantum gravity hinting us toward considering new types of matter? The answers to these questions, that touch the foundations of physics and the very concepts with which we organize our understanding of reality, require in the end of the journey to confront ourselves with empirical data. And for that, the universe itself provides us with the best of possible laboratories.

Quantum generalisation of Einstein’s Equivalence Principle can be verified with entangled clocks as quantum reference frames. (arXiv:2112.03303v3 [quant-ph] UPDATED)

Authors: Carlo CepollaroFlaminia Giacomini

The Einstein Equivalence Principle (EEP) is of crucial importance to test the foundations of general relativity. When the particles involved in the test exhibit quantum properties, it is unknown whether this principle still holds. A possibility introduced in arXiv:2012.13754 is that the EEP holds in a generalised form for particles having an arbitrary quantum state. The core of this proposal is the ability to transform to a Quantum Reference Frame (QRF) associated to an arbitrary quantum state of a physical system, in which the metric is locally inertial. Here, we show that this extended EEP, initially formulated in terms of the local expression of the metric field in a QRF, can be verified in an interferometric setup via tests on the proper time of entangled clocks. We find that the violation of the generalised EEP corresponds to the impossibility of defining dynamical evolution in the frame of each clock. The violation results in a modification to the probabilities of measurements calculated in the laboratory frame, and hence can be verified in an interferometric setting.

Pantheon+ tomography and Hubble tension. (arXiv:2207.10927v2 [astro-ph.CO] UPDATED)

Authors: Deng Wang

The recently released Type Ia supernovae (SNe Ia) sample, Pantheon+, is an updated version of Pantheon and has very important cosmological implications. To explore the origin of the enhanced constraining power and internal correlations of datasets in different redshifts, we perform a comprehensively tomographic analysis of the Pantheon+ sample. Using the Pantheon+ data alone, we give the $2\,\sigma$ lower bound on the Hubble constant $H_0>45.7$ km s$^{-1}$ Mpc$^{-1}$ and the matter fraction $\Omega_m=0.367\pm0.030$, which shows the evidence of dark energy at the $21\,\sigma$ confidence level but is in a $1.7\,\sigma$ tension with that from the Planck-2018 measurement. Combining the Pantheon+ sample with cosmic microwave background, baryon acoustic oscillations, cosmic chronometers, galaxy clustering and weak lensing data, we give the strongest constraint $H_0=67.88\pm0.42$ km s$^{-1}$ Mpc$^{-1}$ at the $1\,\sigma$ confidence level. After dividing the full sample to 10 bins, we find that the first bin in the redshift range $z\in[0.00122, \, 0.227235]$ dominates the constraining power of the whole sample. We also investigate the effects of low-z and high-z subsamples of Pantheon+ on $H_0$ and $\Omega_{m}$, and find that low-z SNe Ia do not have enough constraining power until $z\sim0.1$. Interestingly, high-z SNe Ia in the redshift range $z>0.227235$ can give an competitive constraint on $\Lambda$CDM when compared to three low-z bins. We expect that future high-precision SNe Ia data can independently determine both $H_0$ and $\Omega_{m}$.

Quantifying Nonlocality: How Outperforming Local Quantum Codes Is Expensive

Author(s): Nouédyn Baspin and Anirudh Krishna

Quantum low-density parity-check (LDPC) codes are a promising avenue to reduce the cost of constructing scalable quantum circuits. However, it is unclear how to implement these codes in practice. Seminal results of Bravyi et al. [Phys. Rev. Lett. 104, 050503 (2010)] have shown that quantum LDPC code…

[Phys. Rev. Lett. 129, 050505] Published Thu Jul 28, 2022

Chiral cavity quantum electrodynamics

Nature Physics, Published online: 28 July 2022; doi:10.1038/s41567-022-01671-3

Edge modes in chiral topological systems can carry quantum information without backscattering. A topological lattice of superconducting resonators has been coupled to a qubit, providing a platform for chiral quantum electrodynamics and communication.

Renormalization group methods and the epistemology of effective field theories

Koberinski, Adam and Fraser, Doreen (2022) Renormalization group methods and the epistemology of effective field theories. [Preprint]

A simple proof that the global phase is real

Gao, Shan (2022) A simple proof that the global phase is real. [Preprint]

A broken translational symmetry state in an infinite-layer nickelate

Nature Physics, Published online: 25 July 2022; doi:10.1038/s41567-022-01660-6

Unconventional superconductivity is often associated with the presence of other kinds of electronic order. Observations of charge order in infinite-layer nickelate superconductors show that they fit this pattern.

Prolongments of “Ensaio”: Schrödinger Logics and Quasi-Set Theory

Krause, Décio (2022) Prolongments of “Ensaio”: Schrödinger Logics and Quasi-Set Theory. [Preprint]

On the discrepancies between quantum logic and classical logic

Krause, Décio (2022) On the discrepancies between quantum logic and classical logic. [Preprint]

What is it Like to be a Relativistic GRW Theory? Or: Quantum Mechanics and Relativity, Still in Conflict After All These Years

Allori, Valia (2022) What is it Like to be a Relativistic GRW Theory? Or: Quantum Mechanics and Relativity, Still in Conflict After All These Years. [Preprint]