Quantum Information

When gravity is sourced by a quantum system, there is tension between its role as the mediator of a fundamental interaction, which is expected to acquire nonclassical features, and its role in determining the properties of spacetime, which is inherently classical. Fundamentally, this tension should result in breaking one of the fundamental principles of quantum theory or general relativity, but it is usually hard to assess which one without resorting to a specific model. Here, we answer this question in a theory-independent way using General Probabilistic Theories (GPTs). We consider the interactions of the gravitational field with a single matter system, and derive a no-go theorem showing that when gravity is classical at least one of the following assumptions needs to be violated: (i) Matter degrees of freedom are described by fully non-classical degrees of freedom; (ii) Interactions between matter degrees of freedom and the gravitational field are reversible; (iii) Matter degrees of freedom back-react on the gravitational field. We argue that this implies that theories of classical gravity and quantum matter must be fundamentally irreversible, as is the case in the recent model of Oppenheim et al. Conversely if we require that the interaction between quantum matter and the gravitational field are reversible, then the gravitational field must be non-classical.

We analyze the effect of decoherence, modelled by local quantum channels, on quantum critical states and we find universal properties of the resulting mixed state's entanglement, both between system and environment and within the system. Renyi entropies exhibit volume law scaling with a subleading constant governed by a "g-function" in conformal field theory (CFT), allowing us to define a notion of renormalization group (RG) flow (or "phase transitions") between quantum channels. We also find that the entropy of a subsystem in the decohered state has a subleading logarithmic scaling with subsystem size, and we relate it to correlation functions of boundary condition changing operators in the CFT. Finally, we find that the subsystem entanglement negativity, a measure of quantum correlations within mixed states, can exhibit log scaling or area law based on the RG flow. When the channel corresponds to a marginal perturbation, the coefficient of the log scaling can change continuously with decoherence strength. We illustrate all these possibilities for the critical ground state of the transverse-field Ising model, in which we identify four RG fixed points of dephasing channels and verify the RG flow numerically. Our results are relevant to quantum critical states realized on noisy quantum simulators, in which our predicted entanglement scaling can be probed via shadow tomography methods.

Holography has taught us that spacetime is emergent and its properties depend on the entanglement structure of the dual boundary theory. At the same time, we know that local projective measurements tend to destroy entanglement. This leads to a natural question: what happens to the holographic bulk spacetime if we perform strong local projective measurements on a subsystem $A$ of the boundary? In particular, I will explain the effect of measurements performed both on subsystems of a single CFT in its vacuum state, which is dual to pure AdS spacetime, and on various subsystems of two copies of a CFT in the thermofield double state, which is dual to a double-sided AdS black hole. The post-measurement bulk is cut off by end-of-the-world branes and is dual to the complementary unmeasured subsystem $A^c$. The measurement triggers an entangling/disentangling phase transition in the boundary theory, corresponding to a connected/disconnected phase transition in the bulk dual geometry. Interestingly, the post-measurement bulk includes regions that were part of the entanglement wedge of $A$ before the measurement, signaling a transfer of information from the measured to the unmeasured subsystem analogous to quantum teleportation. Finally, I will discuss open questions and future directions related to our work, with a particular focus on its consequences for the complexity of bulk reconstruction.

We demonstrate that some quantum teleportation protocols exhibit measurement induced phase transitions in Sachdev-Ye-Kitaev model. Namely, Kitaev-Yoshida and Gao-Jafferis-Wall protocols have a phase transition if we apply them at a large projection rate or at a large coupling rate respectively. It is well-known that at small rates they allow teleportation to happen only within a small time-window. We show that at large rates, the system goes into a new steady state, where the teleportation can be performed at any moment. In dual Jackiw-Teitelboim gravity these phase transitions correspond to the formation of an eternal traversable wormhole. In the Kitaev-Yoshida case this novel type of wormhole is supported by continuous projections. Based on https://arxiv.org/abs/2210.03083

Quantum simulation of lattice gauge theory is expected to become a major application of near-term quantum devices. In this presentation, I will talk about a quantum simulation scheme for lattice gauge theories motivated by Measurement-Based Quantum Computation [1], which we call Measurement-Based Quantum Simulation (MBQS). In MBQS, we consider preparing a resource state whose entanglement structure reflects the spacetime structure of the simulated gauge theory. We then consider sequentially measuring qubits in the resource state in a certain adaptive manner, which drives the time evolution in the Hamiltonian lattice gauge theory. It turns out that the resource states we use for MBQS of Wegner’s models possess topological order protected by higher-form symmetries. These higher-form symmetries are also practically useful for error correction to suppress contributions that violate gauge symmetries. We also discuss the relation between the resource state and the partition function of Wegner’s model. This presentation is based on my work with Takuya Okuda [2]. [1] R. Raussendorf and H. J. Briegel, A One-Way Quantum Computer, Phys. Rev. Lett. 86, 5188 (2001) [2] H. Sukeno and T. Okuda, Measurement-based quantum simulation of Abelian lattice gauge theories, arXiv:2210.10908

Within the setting of the AdS/CFT correspondence, we ask about the power of computers in the presence of gravity. We show that there are computations on $n$ qubits which cannot be implemented inside of black holes with entropy less than $O(2^n)$. To establish our claim, we argue computations happening inside the black hole must be implementable in a programmable quantum processor, so long as the inputs and description of the unitary to be run are not too large. We then prove a bound on quantum processors which shows many unitaries cannot be implemented inside the black hole, and further show some of these have short descriptions and act on small systems. These unitaries with short descriptions must be computationally forbidden from happening inside the black hole.

We investigate the link between position-based quantum cryptography (PBQC) and holography established in [May19] using holographic quantum error correcting codes as toy models. If the "temporal" scaling of the AdS metric is inserted by hand into the toy model via the bulk Hamiltonian interaction strength we recover a toy model with consistent causality structure. This leads to an interesting implication between two topics in quantum information: if position-based cryptography is secure against attacks with small entanglement then there are new fundamental lower bounds for resources required for one Hamiltonian to simulate another.

In holographic CFTs satisfying eigenstate thermalization, there is a regime where the operator product expansion can be approximated by a random tensor network. The geometry of the tensor network corresponds to a spatial slice in the holographic dual, with the tensors discretizing the radial direction. In spherically symmetric states in any dimension and more general states in 2d CFT, this leads to a holographic error-correcting code, defined in terms of OPE data, that can be systematically corrected beyond the random tensor approximation. The code is shown to be isometric for light operators outside the horizon, and non-isometric inside, as expected from general arguments about bulk reconstruction. The transition at the horizon occurs due to a subtle breakdown of the Virasoro identity block approximation in states with a complex interior.