arXiv subjects

Jinzhao Wang

Publications and source records attributed to Jinzhao Wang.

At least 19 recordsLinked to original sources

arXiv2026

Unbounded Holevo additivity gaps in finite dimensions

We establish unbounded two-use Holevo additivity gaps in finite dimensions. For each sufficiently large fixed integer $K$ and all sufficiently large $n$, we construct channels $T_n$ with output dimension $K^n$, input dimension $\exp(Θ_K(n^2))$, and \[ χ(T_n^{\otimes2})-2χ(T_n) \ge n\left[\frac{\log_2K}{K}-2\log_2(1+9/K)\right]-O(1/n). \] The gap is linear in output qubits, with an explicit quadratic input-qubit cost and an explicit threshold on $n$. We also obtain channels whose single-use Holevo quantity tends to zero while their two-use Holevo information, and hence classical capacity, diverges. The channels arise from structured tensor products of the complementary mixed-unitary channels used in Collins's free-probabilistic proof. We establish minimum-output-entropy gaps by combining Collins--Youn's product-group Haagerup inequality with Bordenave--Collins's quantitative strong-convergence estimates

quant-ph↗

arXiv2026

Artificial Anisotropy Induced Bound States in the Continuum for Integrated Photonic Waveguide

Bound states in the continuum (BICs) enable counterintuitive light confinement without radiation loss, providing a powerful foundation for integrated photonic waveguides. However, existing BIC waveguides are predominantly realized through geometry-dependent designs, where the BIC condition is restricted to narrowly defined structural parameters, limiting design flexibility and practical applicability. Artificial optical anisotropy is introduced as a new design paradigm for BIC waveguides. Implemented using subwavelength-grating (SWG) metamaterials, continuously tailorable anisotropy provides an independent degree of freedom for deterministically reshaping the radiative continuum, enabling flexible formation and systematic control of BIC waveguides over a broad design space. Anisotropy-engineered symmetry breaking further enables controllable asymmetric radiation and precisely tailored field leakage. This paradigm transforms BIC waveguides from geometry-constrained structures into an anisotropy-engineered platform, establishing a general framework for programmable radiation engineering and next-generation integrated photonic devices.

physics.optics↗

arXiv2025

Estimating time in quantum chaotic systems and black holes

We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation." Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time values. Intuitively, it should become increasingly difficult to estimate the precise value of time by making measurements on the state. We use a quantity called the Fisher information from quantum metrology to quantify the minimum uncertainty in estimating time. Due to unitarity, the uncertainty in the time estimate does not grow with time if we have access to optimal measurements on the full system. Restricting the measurements to act on a small subsystem or to have low computational complexity leads to results expected from equilibration, where the time uncertainty becomes large at late times. With optimal measurements on a subsystem larger than half of the system, we regain the ability to estimate the time very precisely, even at late times. Hawking's calculation for the reduced density matrix of the black hole radiation in semiclassical gravity contradicts our general predictions for unitary quantum chaotic systems. Hawking's state always has a large uncertainty for attempts to estimate the time using the radiation, whereas our general results imply that the uncertainty should become small after the Page time. This gives a new version of the black hole information loss paradox in terms of the time estimation task. By restricting to simple measurements on the radiation, the time uncertainty becomes large. This indicates from a new perspective that the observations of computationally bounded agents are consistent with the semiclassical effective description of gravity.

quant-ph↗

arXiv2025

Alpha-bit state merging

State merging is a fundamental protocol in quantum information theory that generalizes quantum teleportation. Traditionally, it is achieved by local operations on shared entanglement and classical communication. In this work, we study state merging done with alpha-bits, a versatile quantum communication resource weaker than qubits. We study alpha-bit state merging with and without catalytic entanglement, and we find a potential gap between the rates of alpha-bits consumed. In light of our result, we discuss how to interpret entanglement wedge reconstruction in AdS/CFT in terms of alpha-bit state merging

quant-ph↗

arXiv2025

Free mutual information and higher-point OTOCs

We introduce a quantity called the free mutual information (FMI), adapted from concepts in free probability theory, as a new physical measure of quantum chaos. This quantity captures the spreading of a time-evolved operator in the space of all possible operators on the Hilbert space, which is doubly exponential in the number of degrees of freedom. It thus provides a finer notion of operator spreading than the well-understood phenomenon of operator growth in physical space. We derive two central results which apply in any physical system: first, an explicit ``Coulomb gas'' formula for the FMI of two observables $A(t)$ and $B$ in terms of the eigenvalues of the product operator $A(t)B$; and second, a general relation expressing the FMI as a weighted sum of all higher-point out-of-time-ordered correlators (OTOCs). This second result provides a precise information-theoretic interpretation for the higher-point OTOCs as collectively quantifying operator ergodicity and the approach to freeness. This physical interpretation is particularly useful in light of recent progress in experimentally measuring higher-point OTOCs. We identify universal behaviours of the FMI and higher-point OTOCs across a variety of chaotic systems, including random unitary circuits and chaotic spin chains, which indicate that spreading in the doubly exponential operator space is a generic feature of quantum many-body chaos. At the same time, the non-generic behavior of the FMI in various non-chaotic systems, including certain unitary designs, shows that there are cases where an operator spreads in physical space but remains localized in operator space. The FMI is thus a sharper diagnostic of chaos than the standard 4-point OTOC.

quant-ph↗

arXiv2025

What exactly does Bekenstein bound?

The Bekenstein bound posits a maximum entropy for matter with finite energy confined to a spatial region. It is often interpreted as a fundamental limit on the information that can be stored by physical objects. In this work, we test this interpretation by asking whether the Bekenstein bound imposes constraints on a channel's communication capacity, a context in which information can be given a mathematically rigorous and operationally meaningful definition. We study specifically the \emph{Unruh channel} that describes a stationary Alice exciting different species of free scalar fields to send information to an accelerating Bob, who is confined to a Rindler wedge and exposed to the noise of Unruh radiation. We show that the classical and quantum capacities of the Unruh channel obey the Bekenstein bound that pertains to the decoder Bob. In contrast, even at high temperatures, the Unruh channel can transmit a significant number of \emph{zero-bits}, which are quantum communication resources that can be used for quantum identification and many other primitive protocols. Therefore, unlike classical bits and qubits, zero-bits and their associated information processing capability are generally not constrained by the Bekenstein bound. However, we further show that when both the encoder and the decoder are restricted, the Bekenstein bound does constrain the channel capacities, including the zero-bit capacity.

hep-th↗

arXiv2024

Quantum Energy Teleportation versus Information Teleportation

Quantum energy teleportation (QET) is the phenomenon in which locally inaccessible energy is activated as extractable work through collaborative local operations and classical communication (LOCC) with an entangled partner. It closely resembles the more well-known quantum information teleportation (QIT) where quantum information can be sent through an entangled pair with LOCC. It is tempting to ask how QET is related to QIT. Here we report a first study of this connection. Despite the apparent similarity, we show that these two phenomena are not only distinct but moreover are mutually competitive. We show a perturbative trade-off relation between their performance in a thermal entangled chaotic many-body system, in which both QET and QIT are simultaneously implemented through a traversable wormhole in an emergent spacetime. Motivated by this example, we study a generic setup of two entangled qudits and prove a universal non-perturbative trade-off bound. It shows that for any teleportation protocol, the overall performance of QET and QIT together is constrained by the entanglement resource. We discuss some explanations of our results.

quant-ph↗

arXiv2022

Beyond islands: A free probabilistic approach

We give a free probabilistic proposal to compute the fine-grained radiation entropy for an arbitrary bulk radiation state, in the context of the Penington-Shenker-Stanford-Yang (PSSY) model where the gravitational path integral can be implemented with full control. We observe that the replica trick gravitational path integral is combinatorially matching the free multiplicative convolution between the spectra of the gravitational sector and the matter sector respectively. The convolution formula computes the radiation entropy accurately even in cases when the island formula fails to apply. It also helps to justify this gravitational replica trick as a soluble Hausdorff moment problem. We then work out how the free convolution formula can be evaluated using free harmonic analysis, which also gives a new free probabilistic treatment of resolving the separable sample covariance matrix spectrum. The free convolution formula suggests that the quantum information encoded in competing quantum extremal surfaces can be modelled as free random variables in a finite von Neumann algebra. Using the close tie between free probability and random matrix theory, we show that the PSSY model can be described as a random matrix model that is essentially a generalization of Page's model. It is then manifest that the island formula is only applicable when the convolution factorizes in regimes characterized by the one-shot entropies. We further show that the convolution formula can be reorganized to a generalized entropy formula in terms of the relative entropy.

hep-th↗

arXiv2022

The refined quantum extremal surface prescription from the asymptotic equipartition property

Information-theoretic ideas have provided numerous insights in the progress of fundamental physics, especially in our pursuit of quantum gravity. In particular, the holographic entanglement entropy is a very useful tool in studying AdS/CFT, and its efficacy is manifested in the recent black hole page curve calculation. On the other hand, the one-shot information-theoretic entropies, such as the smooth min/max-entropies, are less discussed in AdS/CFT. They are however more fundamental entropy measures from the quantum information perspective and should also play pivotal roles in holography. We combine the technical methods from both quantum information and quantum gravity to put this idea on firm grounds. In particular, we study the quantum extremal surface (QES) prescription that was recently revised to highlight the significance of one-shot entropies in characterizing the QES phase transition. Motivated by the asymptotic equipartition property (AEP), we derive the refined quantum extremal surface prescription for fixed-area states via a novel AEP replica trick, demonstrating the synergy between quantum information and quantum gravity. We further prove that, when restricted to pure bulk marginal states, such corrections do not occur for the higher Rényi entropies of a boundary subregion in fixed-area states, meaning they always have sharp QES transitions. Our path integral derivation suggests that the refinement applies beyond AdS/CFT, and we confirm it in a black hole toy model by showing that the Page curve, for a black hole in a superposition of two radiation stages, receives a large correction that is consistent with the refined QES prescription.

hep-th↗

arXiv2021

The black hole information puzzle and the quantum de Finetti theorem

The black hole information puzzle arises from a discrepancy between conclusions drawn from general relativity and quantum theory about the nature of the radiation emitted by a black hole. According to Hawking's original argument, the radiation is thermal and its entropy thus increases monotonically as the black hole evaporates. Conversely, due to the reversibility of time evolution according to quantum theory, the radiation entropy should start to decrease after a certain time, as predicted by the Page curve. This decrease has been confirmed by new calculations based on the replica trick, which also exhibit its geometrical origin: spacetime wormholes that form between the replicas. Here we analyse the discrepancy between these and Hawking's original conclusions from a quantum information theory viewpoint, using in particular the quantum de Finetti theorem. The theorem implies the existence of extra information, $W$, which is neither part of the black hole nor the radiation, but plays the role of a reference. The entropy obtained via the replica trick can then be identified to be the entropy $S(R|W)$ of the radiation conditioned on the reference $W$, whereas Hawking's original result corresponds to the non-conditional entropy $S(R)$. The entropy $S(R|W)$, which mathematically is an ensemble average, gains an operational meaning in an experiment with $N$ independently prepared black holes: For large $N$, it equals the normalised entropy of their joint radiation, $S(R_1 \cdots R_N)/N$. The discrepancy between this entropy and $S(R)$ implies that the black holes are correlated. The replica wormholes may thus be interpreted as the geometrical representation of this correlation. Our results also suggest a many-black-hole extension of the widely used random unitary model, which we support with non-trivial checks.

hep-th↗

arXiv2021

On the horizon entropy of a causal set

We discuss how to define a kinematical horizon entropy on a causal set. We extend a recent definition of horizon molecules to a setting with a null hypersurface crossing the horizon. We argue that, as opposed to the spacelike case, this extension fails to yield an entropy local to the hypersurface-horizon intersection in the continuum limit when the causal set approximates a curved spacetime. We then investigate the entropy defined via the Spacetime Mutual Information between two regions of a causal diamond truncated by a causal horizon, and find it does limit to the area of the intersection.

gr-qc↗

arXiv2020

Revisiting the equality conditions of the data processing inequality for the sandwiched Rényi divergence

We provide a transparent, simple and unified treatment of recent results on the equality conditions for the data processing inequality (DPI) of the sandwiched quantum Rényi divergence, including the statement that equality in the data processing implies recoverability via the Petz recovery map for the full range of $α$ recently proven by Jen\v cová. We also obtain a new set of equality conditions, generalizing a previous result by Leditzky et al.

quant-ph↗

arXiv2020

On the continuum limit of Benincasa-Dowker-Glaser causal set action

We study the continuum limit of the Benincasa-Dowker-Glaser causal set action on a causally convex compact region. In particular, we compute the action of a causal set randomly sprinkled on a small causal diamond in the presence of arbitrary curvature in various spacetime dimensions. In the continuum limit, we show that the action admits a finite limit. More importantly, the limit is composed by an Einstein-Hilbert bulk term as predicted by the Benincasa-Dowker-Glaser action, and a boundary term exactly proportional to the codimension-two joint volume. Our calculation provides strong evidence in support of the conjecture that the Benincasa-Dowker-Glaser action naturally includes codimension-two boundary terms when evaluated on causally convex regions.

gr-qc↗

arXiv2020

Outer entropy = Bartnik-Bray inner mass, and the gravitational ant conjecture

Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated by the holographic duality, and the Bartnik-Bray quasilocal mass long known in the mathematics community. In both scenarios, one seeks an optimal spacetime fill-in of a given closed, connected, spacelike, codimension-two boundary. We show that for an outer-minimizing mean-convex surface, the Bartnik-Bray inner mass matches exactly with the irreducible mass corresponding to the outer entropy. The equivalence implies that the area laws derived from the outer entropy are mathematically equivalent as the monotonicity property of the quasilocal mass. It also gives rise to new bounds between entropy and the gravitational energy, which naturally gives the gravitational counterpart to Wall's ant conjecture. We also observe that the equality can be achieved in a conformal flow of metrics, which is structurally similar to the Ceyhan-Faulkner proof of the ant conjecture. We compute the small sphere limit of the outer entropy and it is proportional to the bulk stress tensor as one would expect for a quasilocal mass. Lastly, we discuss some implications of taking quantum matter into consideration in the semiclassical setting.

hep-th↗

arXiv2020

The small sphere limit of quasilocal energy in higher dimensions along lightcone cuts

The problem of quasilocal energy has been extensively studied mainly in four dimensions. Here we report results regarding the quasilocal energy in spacetime dimension $n\geq 4$. After generalising three distinct quasilocal energy definitions to higher dimensions under appropriate assumptions, we evaluate their small sphere limits along lightcone cuts shrinking towards the lightcone vertex. The results in vacuum are conveniently represented in terms of the electromagnetic decompositions of the Weyl tensor. We find that the limits at presence of matter yield the stress tensor as expected, but the vacuum limits are in general not proportional to the Bel-Robinson superenergy $Q$ in dimensions $n>4$. The result defies the role of the Bel-Robinson superenergy as characterising the gravitational energy in higher dimensions, albeit the fact that it uniquely generalises. Surprisingly, the Hawking energy and the Brown-York energy exactly agree upon the small sphere limits across all dimensions. The new vacuum limit $\mathcal{Q}$, however, cannot be interpreted as a gravitational energy because of its non-positivity. Furthermore, we also give the small sphere limits of the Kijowski-Epp-Liu-Yau type energy in higher dimensions, and again we see $\mathcal{Q}$ in place of $Q$. Our work extends earlier investigations of the small sphere limits [1, 2, 3, 4], and also complements [5].

gr-qc↗

arXiv2019

Local gravitational energy in higher dimensions

In general relativity, the local gravitational energy is best characterised by the quasilocal mass. The small sphere limit of quasilocal mass provides us the most local notion of gravitational energy. In four dimensions, the limits were shown be the stress tensor in non-vacuum and the Bel-Robinson tensor in vacuum. We study the local gravitational energy in higher dimensions through the lens of the small sphere limits of various quasilocal mass proposals which can be appropriately generalised beyond four dimensions, and report a new quantity $\Q$ which potentially characterises the local gravitational energy content in vacuum. We find that the limits at presence of matter yield the stress tensor as expected, but the vacuum limits are not proportional to the Bel-Robinson superenergy $Q$ in dimensions $n>4$. The result defies the role of the Bel-Robinson superenergy as characterising the gravitational energy in higher dimensions, albeit the fact that it uniquely generalises. More surprisingly, $\Q$ replace the Bel-Robinson superenergy $Q$ in all three quasilocal mass proposals that we study. However, $\Q$ cannot be directly interpreted as a local gravitational energy because of its non-positivity. The physical meaning of $\Q$ awaits more evidence from investigating other quasilocal masses in higher dimensions.

gr-qc↗

arXiv2019

Geometry of small causal diamonds

The geometry of small causal diamonds is systematically studied, based on three distinct constructions that are common in the literature, namely the geodesic ball, the Alexandrov interval and the lightcone cut. The causal diamond geometry is calculated perturbatively using Riemann normal coordinate expansion up to the leading order in both vacuum and non-vacuum. We provide a collection of results including the area of the codimension-two edge, the maximal hypersurface volume and their isoperimetric ratio for each construction, which will be useful for any applications involving the quantitative properties of causal diamonds. In particular, by solving the dynamical equations of the expansion and the shear on the lightcone, we find that intriguingly only the light-cone cut construction yields an area deficit proportional to the Bel-Robinson superenergy density W in four dimensional spacetime, but such a direct connection fails to hold in any other dimension. We also compute the volume of the Alexandrov interval causal diamond in vacuum, which we believe is important but missing from the literatures. Our work complements and extends the earlier works on the causal diamond geometry by Gibbons and Solodukhin, Jacobson, Senovilla and Speranza and others. Some potential applications of our results in mathematical general relativity and quantum gravity are discussed.

gr-qc↗

arXiv2018

Confidence Polytopes in Quantum State Tomography

Quantum State Tomography is the task of inferring the state of a quantum system from measurement data. A reliable tomography scheme should not only report an estimate for that state, but also well-justified error bars. These may be specified in terms of confidence regions, i.e., subsets of the state space which contain the system's state with high probability. Here, building upon a quantum generalisation of Clopper-Pearson confidence intervals--a notion known from classical statistics--we present a simple and reliable scheme for generating confidence regions. These have the shape of a polytope and can be computed efficiently. We provide several examples to demonstrate the practical usability of the scheme in experiments.

quant-ph↗