long vectors
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2015 ◽  
Vol 197 ◽  
pp. 118-127 ◽  
Author(s):  
E. Estevez-Rams ◽  
C. Perez-Demydenko ◽  
B. Aragón Fernández ◽  
R. Lora-Serrano
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Author(s):  
Scott Aaronson

Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n . But using ideas from computational learning theory, we show that one can do exponentially better in a statistical setting. In particular, to predict the outcomes of most measurements drawn from an arbitrary probability distribution, one needs only a number of sample measurements that grows linearly with n . This theorem has the conceptual implication that quantum states, despite being exponentially long vectors, are nevertheless ‘reasonable’ in a learning theory sense. The theorem also has two applications to quantum computing: first, a new simulation of quantum one-way communication protocols and second, the use of trusted classical advice to verify untrusted quantum advice.


1988 ◽  
Vol 8 (1-3) ◽  
pp. 351-361 ◽  
Author(s):  
C.H. Lai ◽  
H.M. Liddell
Keyword(s):  

1986 ◽  
Vol 36 (3) ◽  
pp. 256-275
Author(s):  
Albert G. Buckley
Keyword(s):  

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