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For the two-period quantum walk with the parameters $\\theta_1$ and $\\theta_2$ in the coin operations we show that the standard deviation [$\\sigma_{\\theta_1, \\theta_2} (t)$] is the same as the minimum of standard deviation obtained from one of the one-period quantum walks with coin operations $\\theta_1$ or $\\theta_2$, $\\sigma_{\\theta_1, \\theta_2}(t) = \\min \\{\\sigma_{\\theta_1}(t), \\sigma_{\\theta_2}(t) \\}$. Our numerical result is anal"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1711.05920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-11-16T04:26:34Z","cross_cats_sorted":[],"title_canon_sha256":"60a6490e9e0590924b1bd8cce4ed7318ca2fcb79f5127884ef93a8bf33e64a72","abstract_canon_sha256":"9315558c32349e588e4592a49bf26509c3f85cc5ca36ab5051b807a93bd7e016"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:36.826859Z","signature_b64":"aOp5gO4LR5Y4k5+CMg3itS6lHpyyB/M3/i3k7F56HmzmZYwW0v5WP+N3XZfe7sba0ZIIdwwgnv3Rr2yX5tACBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d631ed273d73eb976ac241c3c66f0d067a0c30de03538bdef3d107e533e3b26","last_reissued_at":"2026-05-18T00:25:36.826153Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:36.826153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"C. M. Chandrashekar, N. Pradeep Kumar, Radhakrishna Balu, Raymond Laflamme","submitted_at":"2017-11-16T04:26:34Z","abstract_excerpt":"We study the dynamics of discrete-time quantum walk using quantum coin operations, $\\hat{C}(\\theta_1)$ and $\\hat{C}(\\theta_2)$ in time-dependent periodic sequence. For the two-period quantum walk with the parameters $\\theta_1$ and $\\theta_2$ in the coin operations we show that the standard deviation [$\\sigma_{\\theta_1, \\theta_2} (t)$] is the same as the minimum of standard deviation obtained from one of the one-period quantum walks with coin operations $\\theta_1$ or $\\theta_2$, $\\sigma_{\\theta_1, \\theta_2}(t) = \\min \\{\\sigma_{\\theta_1}(t), \\sigma_{\\theta_2}(t) \\}$. 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