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SUMMARY:Classical Commitments to Quantum States - Agi Vilanyi (MIT)
DTSTART:20250728T090000Z
DTEND:20250728T100000Z
UID:TALK234415@talks.cam.ac.uk
CONTACT:Tom Gur
DESCRIPTION:We define the notion of a classical commitment scheme to quant
 um states\, which allows a quantum prover to compute a classical commitmen
 t to a quantum state\, and later open each qubit of the state in either th
 e standard or the Hadamard basis. Our notion is a strengthening of the mea
 surement protocol from Mahadev (STOC 2018). We construct such a commitment
  scheme from the post-quantum Learning With Errors (LWE) assumption\, and 
 more generally from any noisy trapdoor claw-free function family that has 
 the distributional strong adaptive\nhardcore bit property (a property that
  we define in this work). Our scheme is succinct in the sense that the run
 ning time of the verifier in the commitment\nphase depends only on the sec
 urity parameter (independent of the size of the committed state)\, and its
  running time in the opening phase grows only with the number of qubits th
 at are being opened (and the security parameter). As a corollary we obtain
  a classical succinct argument system for QMA under the post-quantum LWE a
 ssumption. Previously\, this was only known assuming post-quantum secure i
 ndistinguishability obfuscation. As an additional corollary we obtain a ge
 neric way of converting any X/Z quantum PCP into a succinct argument syste
 m under the quantum hardness of LWE.
LOCATION:Computer Laboratory\, William Gates Building\, Room SS03
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