arXiv subjects

Akash Vijay

Publications and source records attributed to Akash Vijay.

5 recordsLinked to original sources

arXiv2026

Hierarchy of R\'enyi Coherent Information in Stabilizer Codes

R\'enyi coherent information, a computable proxy for the von Neumann coherent information, is widely used to study mixed-state phases of matter and decodability transitions in noisy quantum error-correcting codes. However, being a difference of two R\'enyi entropies, it need not be monotonic in the R\'enyi index, and lacks the operational meaning of its von Neumann counterpart. Here we address both issues for stabilizer codes. First, for Pauli noise generated by independent Bernoulli events, we prove that the R\'enyi-$n$ coherent information is nondecreasing in $n \in \mathbb{Z}^+$. This follows from a general theorem: if independent random bits are mapped linearly to a fine label $T$ and a coarse label $C$, then the R\'enyi entropy difference $H_n(C)-H_n(T)$ is nondecreasing in $n$. For stabilizer codes, $T$ is the joint syndrome--logical class and $C$ is the syndrome, and the difference is the R\'enyi-$n$ coherent information up to a constant. The same theorem covers classical linear codes and independent detector error models. Second, for arbitrary stochastic Pauli noise, we give the R\'enyi-$n$ coherent information an operational meaning via postselection on matching syndromes between one data block and $n-1$ auxiliary blocks. We determine when this defines a quantum channel and show that saturation of the R\'enyi-$n$ coherent information is equivalent to asymptotically perfect recovery of the postselected channel. Moreover, the R\'enyi-$n$ coherent information also upper-bounds the ordinary coherent information achievable after any syndrome-conditioned recovery.

quant-ph↗

arXiv2025

Information Critical Phases under Decoherence

Quantum critical phases are extended regions of phase space characterized by a diverging correlation length. By analogy, we define an \emph{information critical phase} as an extended region of a mixed state phase diagram where the Markov length, the characteristic length scale governing the decay of the conditional mutual information (CMI), diverges. We demonstrate that such a phase arises in decohered $\mathbb{Z}_{N}$ toric codes by assessing both the CMI and the coherent information, the latter quantifying the robustness of the encoded logical qudits. For $N>4$, we find that the system hosts an information critical phase intervening between the decodable and non-decodable phases where the coherent information saturates to a fractional value in the thermodynamic limit, indicating that a finite fraction of logical information is still preserved. We show that the density matrix in this phase can be decomposed into a convex sum of Coulombic pure states, where gapped anyons reorganize into gapless photons. We further consider the ungauged $\mathbb{Z}_{N}$ toric code and interpret its mixed state phase diagram in the language of strong-to-weak spontaneous symmetry breaking. We argue that in the dual model, the information critical phase arises because the spontaneously broken off-diagonal $\mathbb{Z}_{N}$ symmetry gets enhanced to a $U(1)$ symmetry, resulting in a novel superfluid phase whose gapless modes involve coherent excitations of both the system and the environment. Finally, we propose an optimal decoding protocol for the corrupted $\mathbb{Z}_{N}$ toric code and show that its logical error rate saturates to a fractional value in the information critical phase. Our findings identify a gapless analog for mixed-state phases that still acts as a fractional topological quantum memory, thereby extending the conventional paradigm of quantum memory phases.

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arXiv2025

Holographically Emergent Gauge Theory in Symmetric Quantum Circuits

We develop a novel holographic framework to study dynamical phases in random quantum circuits with a global symmetry $G$. Viewing the circuit as a tensor network, we decompose it into two parts: a symmetric layer, which defines an emergent gauge wavefunction in one higher dimension, and a non-symmetric layer, composed of random multiplicity tensors. For $G\,{=}\,\mathbb{Z}_N$ symmetric circuits consisting of local unitary gates interspersed with local symmetric noise channels, averaging over the non-symmetric layer yields a dynamically generated noisy $\mathbb{Z}_{N}$ surface code. This allows us to interpret $\mathbb{Z}_{N}$ symmetric circuits in the volume-law phase as quantum error-correcting codes with a distinguished set of logical spin states that inherit the topological protection of the bulk code. By establishing equality of bulk and boundary coherent information, we show that quantum information encoded in these logical states is maximally protected against symmetric noise up to a finite threshold. We further study weakly monitored $\mathbb{Z}_{N}$ symmetric circuits which exhibit a charge-sharpening transition. We show that the point at which the observer gains classical information about the global charge coincides with the point at which measurements destroy the underlying quantum information encoded in the bulk surface code. This also allows for a natural interpretation of the sharpening transition as a confinement transition in the gauge theory. For $N\,{\leq}\,4$, weak measurements drive a single transition from a charge-fuzzy phase with exponential sharpening time $t_{\#}\sim e^{L}$ to a charge-sharp phase with $t_{\#}\sim \mathcal{O}(1)$. On the other hand, for $N>4$, the circuit can enter an intermediate phase with a linear sharpening time $t_{\#}\sim \mathcal{O}(L)$. In this regime, the bulk gauge theory realizes a Coulomb phase with emergent gapless photons.

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arXiv2025

Analytically Continuing the Randomized Measurement Toolbox

We develop a framework for extracting non-polynomial analytic functions of density matrices in randomized measurement experiments by a method of analytical continuation. A central advantage of this approach, dubbed stabilized analytic continuation (SAC), is its robustness to statistical noise arising from finite repetitions of a quantum experiment, making it well-suited to realistic quantum hardware. As a demonstration, we use SAC to estimate the von Neumann entanglement entropy of a numerically simulated quenched N\'eel state from R\'enyi entropies estimated via the randomized measurement protocol. We then apply the method to experimental R\'enyi data from a trapped-ion quantum simulator experiment, extracting subsystem von Neumann entropies at different evolution times. Finally, we briefly note that the SAC framework is readily generalizable to obtain other nonlinear diagnostics, such as the logarithmic negativity and R\'enyi relative entropies.

quant-ph↗

arXiv2023

Rényi mutual information in quantum field theory, tensor networks, and gravity

We explore a large class of correlation measures called the $α-z$ Rényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, the $α-z$ RMIs are positive semi-definite and monotonically decreasing under quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values of $α$ and $z$, the $α-z$ RMIs also lower bound connected correlation functions. We develop an easily implementable replica trick which enables us to compute the $α-z$ RMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography.

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