Paper 2019/1204

Efficient simulation of random states and random unitaries

Gorjan Alagic, Christian Majenz, and Alexander Russell


We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access. This problem has previously only been considered for restricted adversaries. Against adversaries with an a priori bound on the number of queries, it is well-known that t-designs suffice. Against polynomial-time adversaries, one can use pseudorandom states (PRS) and pseudorandom unitaries (PRU), as defined in a recent work of Ji, Liu, and Song; unfortunately, no provably secure construction is known for PRUs. In our setting, we are concerned with unbounded adversaries. Nonetheless, we are able to give stateful quantum algorithms which simulate the ideal object in both settings of interest. In the case of Haar- random states, our simulator is polynomial-time, has negligible error, and can also simulate verification and reflection through the simulated state. This yields an immediate application to quantum money: a money scheme which is information-theoretically unforgeable and untraceable. In the case of Haar-random unitaries, our simulator takes polynomial space, but simulates both forward and inverse access with zero error. These results can be seen as the first significant steps in developing a theory of lazy sampling for random quantum objects.

Available format(s)
Publication info
Preprint. MINOR revision.
Quantumlazy samplingrandomnessquantum money
Contact author(s)
christian majenz @ cwi nl
galagic @ gmail com
acr @ uconn edu
2019-10-15: received
Short URL
Creative Commons Attribution


      author = {Gorjan Alagic and Christian Majenz and Alexander Russell},
      title = {Efficient simulation of random states and random unitaries},
      howpublished = {Cryptology ePrint Archive, Paper 2019/1204},
      year = {2019},
      note = {\url{}},
      url = {}
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