On the complexity of approximating the diamond norm
Quantum Information & Computation
Computational distinguishability of degradable and antidegradable channels
Quantum Information & Computation
Distinguishing quantum operations having few Kraus operators
Quantum Information & Computation
Quantum commitments from complexity assumptions
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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This paper considers the following problem. Two mixedstate quantum circuits Q驴 and Q驴 are given, and the goal is to determine which of two possibilities holds: (i) Q驴 and Q驴 act nearly identically on all possible quantum state inputs, or (ii) there exists some input state p that Q驴 and Q驴 transform into almost perfectly distinguishable outputs. This may be viewed as an abstraction of the problem that asks, given two discrete quantum mechanical processes described by sequences of local interactions, are the processes effectively the same or are they different? We prove that this promise problem is complete for the class QIP of problems having quantum interactive proof systems, and is therefore PSPACE-hard. This is in contrast to the fact that the analogous problem for classical (probabilistic) circuits is in AM, and for unitary quantum circuits is in QMA.