BEGIN:VCALENDAR PRODID:-//AddEvent Inc//AddEvent.com v1.7//EN VERSION:2.0 BEGIN:VTIMEZONE TZID:America/New_York BEGIN:STANDARD DTSTART:20261101T010000 RRULE:FREQ=YEARLY;BYDAY=1SU;BYMONTH=11 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:EST END:STANDARD BEGIN:DAYLIGHT DTSTART:20260308T030000 RRULE:FREQ=YEARLY;BYDAY=2SU;BYMONTH=3 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT DESCRIPTION:Quantum channel tomography: optimal bounds and a Heisenberg-to-classical phase transition\nKean Chen | University of Pennsylvania\nHow many black-box queries to a quantum channel are needed to learn its full classical description? This question lies at the heart of quantum channel tomography (also known as quantum process tomography)\, a fundamental task in the characterization and validation of quantum hardware. Despite extensive prior work\, the optimal query complexity for quantum channel tomography is far from fully understood.\nIn this paper\, we study tomography of an unknown quantum channel with input dimension d1\, output dimension d2\, and Kraus rank at most r\, to within error ε. We identify the dilation rate τ=rd2/d1 (which always satisfies τ≥1 due to the trace preservation of quantum channels) as a key parameter\, and establish that the optimal query complexity of channel tomography exhibits distinct scaling laws across three regimes of τ.\n- In the boundary regime (τ=1): we show that the query complexity is Θ(rd1d2/ε) for Choi trace norm error ε\, and is upper bounded by O(min{rd1.51d2/ε\,rd1d2/ε2}) and lower bounded by Ω(rd1d2/ε) for diamond norm error ε.\n- In the away-from-boundary regime (τ≥1+Ω(1)): we show that the query complexity is Θ(rd1d2/ε2) for both Choi trace norm and diamond norm errors ε.Our results uncover a sharp Heisenberg-to-classical phase transition in the query complexity of quantum channel tomography: at τ=1\, the optimal query complexity exhibits Heisenberg scaling 1/ε\, whereas for τ≥1+Ω(1)\, it exhibits classical scaling 1/ε2. In addition\, we show that in the near-boundary regime (1 X-ALT-DESC;FMTTYPE=text/html:Quantum channel tomography: optimal bounds and a Heisenberg-to-classical phase transition
Kean Chen | University of Pennsylvania
How many black-box queries to a quantum channel are needed to learn its full classical description? This question lies at the heart of quantum channel tomography (also known as quantum process tomography), a fundamental task in the characterization and validation of quantum hardware. Despite extensive prior work, the optimal query complexity for quantum channel tomography is far from fully understood.
In this paper, we study tomography of an unknown quantum channel with input dimension d1, output dimension d2, and Kraus rank at most r, to within error ε. We identify the dilation rate τ=rd2/d1 (which always satisfies τ≥1 due to the trace preservation of quantum channels) as a key parameter, and establish that the optimal query complexity of channel tomography exhibits distinct scaling laws across three regimes of τ.
- In the boundary regime (τ=1): we show that the query complexity is Θ(rd1d2/ε) for Choi trace norm error ε, and is upper bounded by O(min{rd1.51d2/ε,rd1d2/ε2}) and lower bounded by Ω(rd1d2/ε) for diamond norm error ε.
- In the away-from-boundary regime (τ≥1+Ω(1)): we show that the query complexity is Θ(rd1d2/ε2) for both Choi trace norm and diamond norm errors ε.Our results uncover a sharp Heisenberg-to-classical phase transition in the query complexity of quantum channel tomography: at τ=1, the optimal query complexity exhibits Heisenberg scaling 1/ε, whereas for τ≥1+Ω(1), it exhibits classical scaling 1/ε2. In addition, we show that in the near-boundary regime (1<τ<1+o(1)), the query complexity exhibits a mixture of Heisenberg and classical scaling behaviors.<br />Location
UID:f4493b3fb8914bf4a58dfb8e18b233baaddeventcom SUMMARY:IQC Math and CS seminar featuring Kean Chen DTSTART;TZID=America/New_York:20260715T140000 DTEND;TZID=America/New_York:20260715T150000 DTSTAMP:20260624T211049Z TRANSP:OPAQUE STATUS:CONFIRMED SEQUENCE:0 LOCATION:QNC 4104 X-MICROSOFT-CDO-BUSYSTATUS:BUSY BEGIN:VALARM TRIGGER:-PT30M ACTION:DISPLAY DESCRIPTION:Reminder END:VALARM END:VEVENT END:VCALENDAR