We investigate the relationship between superselection rules and quantum error correcting codes. We demonstrate that the existence of a superselection rule implies the Knill-Laflamme condition in quantum error correction. As an example, we examine the code built from quantum chromodynamics, where the proton and neutron states in the model are explored as different superselection sectors that protect logical information. Finally we comment on topological quantum error correcting codes and supersymmetric quantum field theory within this framework.
", "doi": "10.1007/jhep05(2025)236", "issn": "1029-8479", "publisher": "Springer Science and Business Media LLC", "publication": "Journal of High Energy Physics", "publication_date": "2025-05", "series_number": "5", "volume": "2025", "issue": "5", "pages": "236" }, { "id": "authors:2c7t7-n0570", "collection": "authors", "collection_id": "2c7t7-n0570", "cite_using_url": "https://authors.library.caltech.edu/records/2c7t7-n0570", "type": "article", "title": "Discovery of optimal quantum codes via reinforcement learning", "author": [ { "family_name": "Su", "given_name": "Vincent Paul", "orcid": "0000-0001-7196-4040" }, { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Hu", "given_name": "Hong-Ye", "orcid": "0000-0001-5841-831X" }, { "family_name": "Yanay", "given_name": "Yariv", "orcid": "0000-0002-7214-4156" }, { "family_name": "Tahan", "given_name": "Charles", "orcid": "0000-0001-7726-8329" }, { "family_name": "Swingle", "given_name": "Brian", "orcid": "0000-0003-0334-3108" } ], "abstract": "The design and optimization of quantum codes is generally hard because of the prohibitive computational cost. The recently introduced quantum lego framework provides a powerful method for generating complex quantum error-correcting codes (QECCs) out of simple ones. We gamify this process and unlock a new avenue for code design and discovery using reinforcement learning (RL). Already for simple code measures and modest qubit numbers, we produce codes that are both optimal and novel. Moreover, we argue that this framework is both scalable, when combined with efficient tensor contraction methods, and flexible, since we can specify arbitrary properties of the code to be optimized. We train on two such properties, maximizing the code distance, and minimizing the probability of logical error under biased Pauli noise. For the first, we show that the trained agent identifies ways to increase code distance beyond naive concatenation, saturating the linear programming bound for CSS (Calderbank, Shor, Steane) codes on 13 qubits. With a learning objective to minimize the logical error probability under biased Pauli noise, we find the best-known CSS code at this task for \u227220 qubits. Compared to other (locally deformed) CSS codes, including Surface, XZZX, and two-dimensional Color codes, our [[17,1,3]] code construction actually has lower adversarial distance, yet better protects the logical information, highlighting the importance of QECC desiderata. Lastly, we comment on how this RL framework can be used in conjunction with physical quantum devices to tailor a code without explicit characterization of the noise model.
", "doi": "10.1103/physrevapplied.23.034048", "issn": "2331-7019", "publisher": "American Physical Society", "publication": "Physical Review Applied", "publication_date": "2025-03-20", "series_number": "3", "volume": "23", "issue": "3", "pages": "034048" }, { "id": "authors:k3pas-bgd22", "collection": "authors", "collection_id": "k3pas-bgd22", "cite_using_url": "https://authors.library.caltech.edu/records/k3pas-bgd22", "type": "article", "title": "Non-trivial area operators require non-local magic", "author": [ { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" } ], "abstract": "We show that no stabilizer codes over any local dimension can support a non-trivial area operator for any bipartition of the physical degrees of freedom even if certain code subalgebras contain non-trivial centers. This conclusion also extends to more general quantum codes whose logical operators satisfy certain factorization properties, including any complementary code that encodes qubits and supports transversal logical gates that form a nice unitary basis. These results support the observation that some desirable conditions for fault tolerance are in tension with emergent gravity and suggest that non-local \"magic\" would play an important role in reproducing features of gravitational back-reaction and the quantum extremal surface formula. We comment on conditions needed to circumvent the no-go result and examine some simple instances of non-stabilizer codes that do have non-trivial area operators.
", "doi": "10.1007/jhep11(2024)105", "issn": "1029-8479", "publisher": "Springer Science and Business Media LLC", "publication": "Journal of High Energy Physics", "publication_date": "2024-11", "series_number": "11", "volume": "2024", "issue": "11", "pages": "105" }, { "id": "authors:f48st-aex88", "collection": "authors", "collection_id": "f48st-aex88", "cite_using_url": "https://authors.library.caltech.edu/records/f48st-aex88", "type": "article", "title": "Quantum Lego Expansion Pack: Enumerators from Tensor Networks", "author": [ { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Gullans", "given_name": "Michael J." }, { "family_name": "Lackey", "given_name": "Brad" }, { "family_name": "Wang", "given_name": "Zitao" } ], "abstract": "We provide the first tensor-network method for computing quantum weight enumerator polynomials in the most general form. If a quantum code has a known tensor-network construction of its encoding map, our method is far more efficient, and in some cases exponentially faster than the existing approach. As a corollary, it produces decoders and an algorithm that computes the code distance. For non-(Pauli)-stabilizer codes, this constitutes the current best algorithm for computing the code distance. For degenerate stabilizer codes, it can be substantially faster compared to the current methods. We also introduce novel weight enumerators and their applications. In particular, we show that these enumerators can be used to compute logical error rates exactly and thus construct (optimal) decoders for any independent and identically distributed single qubit or qudit error channels. The enumerators also provide a more efficient method for computing nonstabilizerness in quantum many-body states. As the power for these speedups rely on a quantum Lego decomposition of quantum codes, we further provide systematic methods for decomposing quantum codes and graph states into a modular construction for which our technique applies. As a proof of principle, we perform exact analyses of the deformed surface codes, the holographic pentagon code, and the two-dimensional Bacon-Shor code under (biased) Pauli noise and limited instances of coherent error at sizes that are inaccessible by brute force.\n \n \n \n \n Published by the American Physical Society\n 2024", "doi": "10.1103/prxquantum.5.030313", "issn": "2691-3399", "publisher": "American Physical Society", "publication": "PRX Quantum", "publication_date": "2024-07-22", "series_number": "3", "volume": "5", "issue": "3", "pages": "030313" }, { "id": "authors:ry5h5-d6y89", "collection": "authors", "collection_id": "ry5h5-d6y89", "cite_using_url": "https://authors.library.caltech.edu/records/ry5h5-d6y89", "type": "article", "title": "Large N matrix quantum mechanics as a quantum memory", "author": [ { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Cheng", "given_name": "Gong", "orcid": "0009-0008-9158-7404", "clpid": "Cheng-Gong" }, { "family_name": "Swingle", "given_name": "Brian", "orcid": "0000-0003-0334-3108", "clpid": "Swingle-Brian" } ], "abstract": "In this paper, we explore the possibility of building a quantum memory that is robust to thermal noise using large N matrix quantum mechanics models. First, we investigate the gauged SU(N) matrix harmonic oscillator and different ways to encode quantum information in it. By calculating the mutual information between the system and a reference which purifies the encoded information, we identify a transition temperature, T_c, below which the encoded quantum information is protected from thermal noise for a memory time scaling as N\u00b2. Conversely, for temperatures higher than T_c, the information is quickly destroyed by thermal noise. Second, we relax the requirement of gauge invariance and study a matrix harmonic oscillator model with only global symmetry. Finally, we further relax even the symmetry requirement and propose a model that consists of a large number N\u00b2 of qubits, with interactions derived from an approximate SU(N) symmetry. In both ungauged models, we find that the effects of gauging can be mimicked using an energy penalty to give a similar result for the memory time. The final qubit model also has the potential to be realized in the laboratory.
", "doi": "10.1103/physrevd.108.086008", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2023-10-15", "series_number": "8", "volume": "108", "issue": "8", "pages": "086008" }, { "id": "authors:3abrh-f1240", "collection": "authors", "collection_id": "3abrh-f1240", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201216-103316521", "type": "article", "title": "Building bulk geometry from the tensor Radon transform", "author": [ { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Qi", "given_name": "Xiao-Liang", "clpid": "Qi-Xiao-Liang" }, { "family_name": "Swingle", "given_name": "Brian", "orcid": "0000-0003-0334-3108", "clpid": "Swingle-Brian" }, { "family_name": "Tang", "given_name": "Eugene", "clpid": "Tang-Eugene" } ], "abstract": "Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of AdS\u2083/CFT\u2082. We find that, given the boundary entanglement entropies of a 2d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative (near AdS) limit. In the case where a well-defined bulk geometry exists, we explicitly reconstruct the unique bulk metric tensor once a gauge choice is made. We then examine the emergent bulk geometries for static and dynamical scenarios in holography and in many-body systems. Apart from the physics results, our work demonstrates that numerical methods are feasible and effective in the study of bulk reconstruction in AdS/CFT.", "doi": "10.1007/JHEP12(2020)033", "issn": "1126-6708", "publisher": "Springer", "publication": "Journal of High Energy Physics", "publication_date": "2020-12", "series_number": "12", "volume": "2020", "issue": "12", "pages": "Art. No. 33" }, { "id": "authors:htz2k-4gv03", "collection": "authors", "collection_id": "htz2k-4gv03", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190709-152651012", "type": "article", "title": "How Low Can Vacuum Energy Go When Your Fields Are Finite-Dimensional?", "author": [ { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Chatwin-Davies", "given_name": "Aidan", "orcid": "0000-0003-1406-9271", "clpid": "Chatwin-Davies-A" }, { "family_name": "Singh", "given_name": "Ashmeet", "orcid": "0000-0002-4404-1416", "clpid": "Singh-Ashmeet" } ], "abstract": "According to the holographic bound, there is only a finite density of degrees of freedom in space when gravity is taken into account. Conventional quantum field theory does not conform to this bound, since in this framework, infinitely many degrees of freedom may be localized to any given region of space. In this paper, we explore the viewpoint that quantum field theory may emerge from an underlying theory that is locally finite-dimensional, and we construct a locally finite-dimensional version of a Klein\u2013Gordon scalar field using generalized Clifford algebras. Demanding that the finite-dimensional field operators obey a suitable version of the canonical commutation relations makes this construction essentially unique. We then find that enforcing local finite dimensionality in a holographically consistent way leads to a huge suppression of the quantum contribution to vacuum energy, to the point that the theoretical prediction becomes plausibly consistent with observations.", "doi": "10.1142/S0218271819440061", "issn": "0218-2718", "publisher": "World Scientific Publishing", "publication": "International Journal of Modern Physics D", "publication_date": "2019-10", "series_number": "14", "volume": "28", "issue": "14", "pages": "Art. No. 1944006" }, { "id": "authors:rr3er-x6z29", "collection": "authors", "collection_id": "rr3er-x6z29", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190820-131613485", "type": "article", "title": "Towards bulk metric reconstruction from extremal area variations", "author": [ { "family_name": "Bao", "given_name": "Ning", "orcid": "0000-0002-3296-1039", "clpid": "Bao-Ning" }, { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Fischetti", "given_name": "Sebastian", "orcid": "0000-0002-2783-211X", "clpid": "Fischetti-S" }, { "family_name": "Keeler", "given_name": "Cynthia", "orcid": "0000-0002-4248-3704", "clpid": "Keeler-C" } ], "abstract": "The Ryu\u2013Takayanagi and Hubeny\u2013Rangamani\u2013Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension d \u2a7e 4, knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an explicitspacetime metric reconstruction.", "doi": "10.1088/1361-6382/ab377f", "issn": "0264-9381", "publisher": "IOP", "publication": "Classical and Quantum Gravity", "publication_date": "2019-09-19", "series_number": "18", "volume": "36", "issue": "18", "pages": "Art. No. 185002" }, { "id": "authors:2m2vx-01829", "collection": "authors", "collection_id": "2m2vx-01829", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171214-111114409", "type": "article", "title": "Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space", "author": [ { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" } ], "abstract": "We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's \"entanglement equilibrium\" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.", "doi": "10.1103/PhysRevD.97.086003", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2018-04-15", "series_number": "8", "volume": "97", "issue": "8", "pages": "Art. No. 086003" }, { "id": "authors:15h82-hak05", "collection": "authors", "collection_id": "15h82-hak05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180105-090200316", "type": "article", "title": "de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity", "author": [ { "family_name": "Bao", "given_name": "Ning", "orcid": "0000-0002-3296-1039", "clpid": "Bao-Ning" }, { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" }, { "family_name": "Chatwin-Davies", "given_name": "Aidan", "orcid": "0000-0003-1406-9271", "clpid": "Chatwin-Davies-A" } ], "abstract": "We investigate the proposed connection between de Sitter spacetime and the multiscale entanglement renormalization ansatz (MERA) tensor network, and ask what can be learned via such a construction. We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter space. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overall Hilbert space is infinite dimensional) or, with certain specific modifications to the tensor structure, a strong form (the entire theory describes only a single patch plus its horizon, in a finite-dimensional Hilbert space). We also suggest that de Sitter evolution has an interpretation in terms of circuit complexity, as has been conjectured for anti\u2013de Sitter space.", "doi": "10.1103/PhysRevD.96.123536", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2017-12-15", "series_number": "12", "volume": "96", "issue": "12", "pages": "Art. No. 123536" }, { "id": "authors:85wjh-qxt55", "collection": "authors", "collection_id": "85wjh-qxt55", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170209-150222935", "type": "article", "title": "Axion detection via Topological Casimir Effect", "author": [ { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Zhitnitsky", "given_name": "Ariel", "clpid": "Zhitnitsky-A-R" } ], "abstract": "We propose a new table-top experimental configuration for the direct detection of dark matter QCD axions in the traditional open mass window 10^(-6)\u2009\u2009eV \u2272 m_a \u2272 10^(-2)\u2009\u2009eV using nonperturbative effects in a system with nontrivial spatial topology. Different from most experimental setups found in literature on direct dark matter axion detection, which relies on \u02d9\u03b8 or \u20d7\u2207\u03b8, we found that our system is in principle sensitive to a static \u03b8 \u2265 10^(-14) and can also be used to set limit on the fundamental constant \u03b8_(QED) which becomes the fundamental observable parameter of the Maxwell system if some conditions are met. Furthermore, the proposed experiments can probe entire open mass window 10^(-6)\u2009\u2009eV \u2272 m_a \u227210^(-2)\u2009\u2009eV with the same design, which should be contrasted with conventional cavity-type experiments being sensitive to a specific axion mass. Connection with Witten effect when the induced electric charge e\u2032 is proportional to \u03b8 and the magnetic monopole becomes the dyon with nonvanishing e\u2032 = -e\u03b8/2\u03c0 is also discussed.", "doi": "10.1103/PhysRevD.96.015013", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2017-07-01", "series_number": "1", "volume": "96", "issue": "1", "pages": "Art. No. 015013" }, { "id": "authors:9x3hm-03b32", "collection": "authors", "collection_id": "9x3hm-03b32", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170228-191741490", "type": "monograph", "title": "Quantum Circuit Cosmology: The Expansion of the Universe Since the First Qubit", "author": [ { "family_name": "Bao", "given_name": "Ning", "orcid": "0000-0002-3296-1039", "clpid": "Bao-Ning" }, { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" }, { "family_name": "McAllister", "given_name": "Liam", "clpid": "McAllister-L" } ], "abstract": "We consider cosmological evolution from the perspective of quantum\ninformation. We present a quantum circuit model for the expansion of a comoving\nregion of space, in which initially-unentangled ancilla qubits become entangled\nas expansion proceeds. We apply this model to the comoving region that now\ncoincides with our Hubble volume, taking the number of entangled degrees of\nfreedom in this region to be proportional to the de Sitter entropy. The quantum\ncircuit model is applicable for at most 140 e-folds of inflationary and\npost-inflationary expansion: we argue that no geometric description was\npossible before the time t_1 when our comoving region was one Planck length\nacross, and contained one pair of entangled degrees of freedom. This approach\ncould provide a framework for modeling the initial state of inflationary\nperturbations.", "doi": "10.48550/arXiv.1702.06959", "publisher": "arXiv", "publication_date": "2017-02-22" }, { "id": "authors:957ax-76c67", "collection": "authors", "collection_id": "957ax-76c67", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160704-200753575", "type": "article", "title": "Space from Hilbert Space: Recovering Geometry from Bulk Entanglement", "author": [ { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" }, { "family_name": "Michalakis", "given_name": "Spyridon", "orcid": "0000-0003-4963-1156", "clpid": "Michalakis-S" } ], "abstract": "We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor product of factors, we consider a class of \"redundancy-constrained states\" in H that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein's equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, though the entropy (and the maximum change thereof) scales like the area of the boundary. A version of the ER=EPR conjecture is recovered, in that perturbations that entangle distant parts of the emergent geometry generate a configuration that may be considered as a highly quantum wormhole.", "doi": "10.1103/PhysRevD.95.024031", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2017-01-15", "series_number": "2", "volume": "95", "issue": "2", "pages": "Art. No. 024031" }, { "id": "authors:h21bb-s9q51", "collection": "authors", "collection_id": "h21bb-s9q51", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160426-103346757", "type": "article", "title": "Aharonov-Bohm phases in a quantum LC circuit", "author": [ { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Yao", "given_name": "Yuan", "clpid": "Yao-Yuan" }, { "family_name": "Zhitnitsky", "given_name": "Ariel R.", "clpid": "Zhitnitsky-A-R" } ], "abstract": "We study novel types of contributions to the partition function of the Maxwell system defined on a small compact manifold. These contributions, often not addressed in the perturbative treatment with physical photons, emerge as a result of tunneling transitions between topologically distinct but physically identical vacuum winding states. These new terms give an extra contribution to the Casimir pressure, yet to be measured. We argue that this effect is highly sensitive to a small external electric field, which should be contrasted with the conventional Casimir effect, where the vacuum photons are essentially unaffected by any external field. Furthermore, photons will be emitted from the vacuum in response to a time-dependent electric field, similar to the dynamical Casimir effect in which real particles are radiated from the vacuum due to the time-dependent boundary conditions. We also propose an experimental setup using a quantum LC circuit to detect this novel effect. We expect physical electric charges to appear on the capacitor plates when the system dimension is such that coherent Aharonov-Bohm phases can be maintained over macroscopically large distances.", "doi": "10.1103/PhysRevD.93.065049", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2016-03-15", "series_number": "6", "volume": "93", "issue": "6", "pages": "Art. No. 065049" }, { "id": "authors:m2vmw-r4x37", "collection": "authors", "collection_id": "m2vmw-r4x37", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150812-144213214", "type": "article", "title": "Holographic entropy inequalities and gapped phases of matter", "author": [ { "family_name": "Bao", "given_name": "Ning", "orcid": "0000-0002-3296-1039", "clpid": "Bao-Ning" }, { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Walter", "given_name": "Michael", "clpid": "Walter-M" }, { "family_name": "Wang", "given_name": "Zitao", "orcid": "0000-0002-2326-2674", "clpid": "Wang-Zitao" } ], "abstract": "We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the \"cyclic inequalities\" derived recently for the holo-graphic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.", "doi": "10.1007/JHEP09(2015)203", "issn": "1126-6708", "publisher": "Springer", "publication": "Journal of High Energy Physics", "publication_date": "2015-09", "series_number": "9", "volume": "2015", "issue": "9", "pages": "Art. No. 203" }, { "id": "authors:c0qbf-wrx40", "collection": "authors", "collection_id": "c0qbf-wrx40", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150601-131525807", "type": "article", "title": "Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence", "author": [ { "family_name": "Bao", "given_name": "Ning", "orcid": "0000-0002-3296-1039", "clpid": "Bao-Ning" }, { "family_name": "Cao", "given_name": "ChunJun", "orcid": "0000-0002-5761-5474", "clpid": "Cao-ChunJun" }, { "family_name": "Carroll", "given_name": "Sean M.", "orcid": "0000-0002-4226-5758", "clpid": "Carroll-S-M" }, { "family_name": "Chatwin-Davies", "given_name": "Aidan", "orcid": "0000-0003-1406-9271", "clpid": "Chatwin-Davies-A" }, { "family_name": "Hunter-Jones", "given_name": "Nicholas", "clpid": "Hunter-Jones-N" }, { "family_name": "Pollack", "given_name": "Jason", "orcid": "0000-0003-4754-4905", "clpid": "Pollack-J-A" }, { "family_name": "Remmen", "given_name": "Grant N.", "orcid": "0000-0001-6569-8866", "clpid": "Remmen-G-N" } ], "abstract": "The multiscale entanglement renormalization ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state of a critical quantum system. The network geometry resembles a discretization of spatial slices of an anti\u2013de Sitter (AdS) spacetime and \"geodesics\" in the MERA reproduce the Ryu-Takayanagi formula for the entanglement entropy of a boundary region in terms of bulk properties. It has therefore been suggested that there could be an AdS/MERA correspondence, relating states in the Hilbert space of the boundary quantum system to ones defined on the bulk lattice. Here we investigate this proposal and derive necessary conditions for it to apply, using geometric features and entropy inequalities that we expect to hold in the bulk. We show that, perhaps unsurprisingly, the MERA lattice can only describe physics on length scales larger than the AdS radius. Further, using the covariant entropy bound in the bulk, we show that there are no conventional MERA parameters that completely reproduce bulk physics even on super-AdS scales. We suggest modifications or generalizations of this kind of tensor network that may be able to provide a more robust correspondence.", "doi": "10.1103/PhysRevD.91.125036", "issn": "1550-7998", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2015-06-29", "series_number": "12", "volume": "91", "issue": "12", "pages": "Art. No. 125036" } ]