An official website of the United States government
In the quantum compression scheme proposed by Schumacher, Alice compresses a message that Bob decompresses. In that approach, there is some probability of failure and, even when successful, some distortion of the state. For sufficiently large blocklengths, both of these imperfections can be made arbitrarily small while achieving a compression rate that asymp- totically approaches the source coding bound. However, direct implementation of Schumacher compression suffers from poor circuit complexity. In this paper, we consider a slightly different approach based on classical syndrome source coding. The idea is to use a linear error-correcting code and treat the state to be compressed as a superposition of error patterns. Then, Alice can use quantum gates to apply the parity-check matrix to her message state. This will convert it into a superposition of syndromes. If the original superposition was supported on correctable errors (e.g., coset leaders), then this process can be reversed by decoding. An implementation of this based on polar codes is described and simulated. As in classical source coding based on polar codes, Alice maps the information into the “frozen” qubits that constitute the syndrome. To decompress, Bob utilizes a quantum version of successive cancellation coding.
more »
« less
M-theory, black holes and cosmology
This paper is dedicated to Michael J. Duff on the occasion of his 70th birthday. I discuss some issues of M-theory/string theory/supergravity closely related to Mike’s interests. I describe a relation between STU black hole entropy, the Cayley hyperdeterminant, the Bhargava cube and a three-qubit Alice–Bob–Charlie triality symmetry. I shortly describe my recent work with Gunaydin, Linde and Yamada on M-theory cosmology (Gunaydin et al. 2020 M-theory cosmology, octonions, error-correcting codes ( http://arxiv.org/abs/2008.01494 )), inspired by the work of Duff with Ferrara and Borsten, Levay, Marrani et al. Here, we have seven-qubits, a party including Alice, Bob, Charlie, Daisy, Emma, Fred and George. Octonions and Hamming error-correcting codes are at the base of these models. They lead to seven benchmark targets of future cosmic microwave background missions looking for primordial gravitational waves from inflation. I also show puzzling relations between the fermion mass eigenvalues in these cosmological models, the exceptional Jordan eigenvalue problem and black hole entropy. The symmetry of our cosmological models is illustrated by beautiful pictures of a Coxeter projection of the root system of E7.
more »
« less
- Award ID(s):
- 2014215
- PAR ID:
- 10284221
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 477
- Issue:
- 2245
- ISSN:
- 1364-5021
- Page Range / eLocation ID:
- 20200786
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A bstract The extended black hole thermodynamics in which the cosmological constant plays the role of pressure significantly enriches the phase structure of the theory. In order to understand the extended black hole thermodynamics more precisely, we let the value of the cosmological constant vary dynamically via tunneling from one vacuum to another in a black hole induced vacuum decay. In this process, entropy of the matter/energy released by a black hole is crucial to validate the second law of thermodynamics. In other words, without taking this bulk entropy into account, entropy associated with the black hole and cosmological horizons may not always increase. Since the bulk entropy is not represented by the black hole and the cosmological horizons, this result calls for a more careful interpretation of the holographic principle in which environmental effects are taken into account.more » « less
-
We experimentally demonstrate that we can detect correlated errors in a twin-field quantum key distribution (TFQKD) system by using a technique that is related to self-consistent tomography. We implement a TFQKD system based on a fiber-Sagnac loop, in which Alice and Bob encode information in the phase of weak coherent states that propagate in opposite directions around the loop. These states interfere as they exit the loop and are detected by a third party, Charlie, who reports the results of their measurements to Alice and Bob. We find that it is possible for Alice and Bob to detect correlated state-preparation and measurement errors while trusting only their own individual states, and without trusting Charlie’s measurements.more » « less
-
Cryptographic protocols are often implemented at upper layers of communication networks, while error-correcting codes are employed at the physical layer. In this paper, we consider utilizing readily-available physical layer functions, such as encoders and decoders, together with shared keys to provide a threshold-type security scheme. To this end, the effect of physical layer communication is abstracted out and the channels between the legitimate parties, Alice and Bob, and the eaves-dropper Eve are assumed to be noiseless. We introduce a model for threshold-secure coding, where Alice and Bob communicate using a shared key in such a way that Eve does not get any information, in an information-theoretic sense, about the key as well as about any subset of the input symbols of size up to a certain threshold. Then, a framework is provided for constructing threshold-secure codes form linear block codes while characterizing the requirements to satisfy the reliability and security conditions. Moreover, we propose a threshold-secure coding scheme, based on Reed-Muller (RM) codes, that meets security and reliability conditions. Furthermore, it is shown that the encoder and the decoder of the scheme can be implemented efficiently with quasi-linear time complexity. In particular, a low-complexity successive cancellation decoder is shown for the RM-based scheme. Also, the scheme is flexible and can be adapted given any key length.more » « less
-
null (Ed.)A bstract We study M-theory compactified on twisted 7-tori with G 2 -holonomy. The effective 4d supergravity has 7 chiral multiplets, each with a unit logarithmic Kähler potential. We propose octonion, Fano plane based superpotentials, codifying the error correcting Hamming (4, 7) code. The corresponding 7-moduli models have Minkowski vacua with one flat direction. We also propose superpotentials based on octonions/error correcting codes for Minkowski vacua models with two flat directions. We update phenomenological α -attractor models of inflation with 3 α = 7 , 6 , 5 , 4 , 3 , 1, based on inflation along these flat directions. These inflationary models reproduce the benchmark targets for detecting B-modes, predicting 7 different values of $$ r=12\alpha /{N}_e^2 $$ r = 12 α / N e 2 in the range 10 − 2 ≳ r ≳ 10 − 3 , to be explored by future cosmological observations.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2020.0786
