Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear programming bounds for quantum amplitude damping codes   Given that approximate quantum error-correcting (AQEC) codes have a
potentially better performance than perfect quantum error correction codes, it
is pertinent to quantify their performance. While quantum weight enumerators
establish some of the best upper bounds on the minimum distance of quantum
error-correcting codes, these bounds do not directly apply to AQEC codes.
Herein, we introduce quantum weight enumerators for amplitude damping (AD)
errors and work within the framework of approximate quantum error correction.
In particular, we introduce an auxiliary exact weight enumerator that is
intrinsic to a code space and moreover, we establish a linear relationship
between the quantum weight enumerators for AD errors and this auxiliary exact
weight enumerator. This allows us to establish a linear program that is
infeasible only when AQEC AD codes with corresponding parameters do not exist.
To illustrate our linear program, we numerically rule out the existence of
three-qubit AD codes that are capable of correcting an arbitrary AD error.

16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org