Block synchronization for quantum information

Abstract

Locating the boundaries of consecutive blocks of quantum information is a fundamental building block for advanced quantum computation and quantum communication systems. We develop a coding theoretic method for properly locating boundaries of quantum information without relying on external synchronization when block synchronization is lost. The method also protects qubits from decoherence in a manner similar to conventional quantum error-correcting codes, seamlessly achieving synchronization recovery and error correction. A family of quantum codes that are simultaneously synchronizable and error-correcting is given through this approach.

Algebraic techniques in designing quantum synchronizable codes

“…In this section we briefly review the mechanism of quantum synchronizable codes introduced in [2] and prove a lemma, which we will use in Sec. III.…”

“…where |χ is the (n − k 2 )-qubit syndrome by S Z D (see [2] for a rigorous proof). If E introduced at most…”

“…Let C be a dual-containing cyclic code of length n and dimension k 1 and D a C-containing cyclic code of the same length, larger dimension k 2 > k 1 , and minimum distance d 2 …”

“…This can be done by running backwards the translation and expansion operations we applied to |ϕ enc and then applying a decoding circuit of the CSS code based on the dual-containing cyclic code C (see [2] for details).…”

Two new families of quantum synchronizable codes

“…[1,2] for the basics of block synchronization techniques in classical digital communications). Quantum block synchronization is also significant because the block structure is typically used in quantum information coding [3,4] as in classical domain and procedures for manipulating it demand precise alignment [5][6][7]. However, since measurement of qubits usually destroys their contained quantum information, quantum analogues of above methods don't apply.…”