Discriminating States: The Quantum Chernoff Bound
نویسندگان
چکیده
منابع مشابه
Discriminating States: the quantum Chernoff bound.
We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the minimal probability of error. This leads to the identification of the quantum Chernoff bound, thereby solving a long-standing open problem. The bound reduces to the classical Chernoff bound when the quantum states under consideration commute. The quantum Chernof...
متن کاملDiscriminating quantum states: the multiple Chernoff distance
We consider the problem of testing multiple quantum hypotheses {ρ 1 , . . . , ρ r }, where an arbitrary prior distribution is given and each of the r hypotheses is n copies of a quantum state. It is known that the minimal average error probability Pe decays exponentially to zero, that is, Pe = exp{−ξn+ o(n)}. However, this error exponent ξ is generally unknown, except for the case that r = 2. I...
متن کاملAttainment of the multiple quantum Chernoff bound for certain ensembles of mixed states
We consider the problem of detecting the true quantum state among r possible ones, based on measurements performed on n of copies of a finite dimensional quantum system. It is known that the exponent for the rate of decrease of the averaged error probability cannot exceed the multiple quantum Chernoff bound (MQCB) defined as the worst case (smallest) quantum Chernoff distance between any possib...
متن کاملOn the Chernoff bound for efficiency of quantum hypothesis testing
The paper estimates the Chernoff rate for the efficiency of quantum hypothesis testing. For both joint and separable measurements, approximate bounds for the rate are given if both states are mixed and exact expressions are derived if at least one of the states is pure. The efficiency of tests with separable measurements is found to be close to the efficiency of tests with joint measurements. T...
متن کامل3 Chernoff Bound
Before we venture into Chernoff bound, let us recall Chebyshev's inequality which gives a simple bound on the probability that a random variable deviates from its expected value by a certain amount.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2007
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.98.160501