Direct measurement of large-scale quantum states via expectation values of non-Hermitian matrices
نویسندگان
چکیده
In quantum mechanics, predictions are made by way of calculating expectation values of observables, which take the form of Hermitian operators. Non-Hermitian operators, however, are not necessarily devoid of physical significance, and they can play a crucial role in the characterization of quantum states. Here we show that the expectation values of a particular set of non-Hermitian matrices, which we call column operators, directly yield the complex coefficients of a quantum state vector. We provide a definition of the state vector in terms of measurable quantities by decomposing these column operators into observables. The technique we propose renders very-large-scale quantum states significantly more accessible in the laboratory, as we demonstrate by experimentally characterizing a 100,000-dimensional entangled state. This represents an improvement of two orders of magnitude with respect to previous phase-and-amplitude characterizations of discrete entangled states.
منابع مشابه
The Role of Heat Bath and Pointer Modes in Quantum Measurement
We present an exact derivation of a process in which a microscopic measured system interacts with " heat bath " and pointer modes of a measuring device, via a linear coupling involving Hermitian operator Λ of the system. In the limit of strong interaction with these modes, over a small time interval , we show that the measured system and the " pointer " part of the measuring device evolve into ...
متن کاملM ar 1 99 9 Quantum Measurement : A Solvable Model
We present an exact derivation of a process in which a microscopic measured system interacts with " heat bath " and pointer modes of a measuring device, via a linear coupling involving Hermitian operator Λ of the system. In the limit of strong interaction with these modes, over a small time interval , we show that the measured system and the " pointer " part of the measuring device evolve into ...
متن کاملHermitian metric on quantum spheres
The paper deal with non-commutative geometry. The notion of quantumspheres was introduced by podles. Here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.
متن کاملاثر درهمتنیدگی و چهارچوب نالخت در بازی کوانتومی چهارکیوبیتی
The effect of increasing quantum bits and Unruh effect on quantum Prisoners’ dilemma has been investigated for both entangled and unentangled initial states. The Nash equilibrium, as an important result of quantum game theory, was obtained through the different payoffs resulted from choosing various strategies. It has been shown that the non-inertial frame disturbs the symmetry of the game. Act...
متن کاملNon-Equilibrium Statistical Quantum Field Theory ( QFT ) and Quantum Optics( QED )
1 Single System 5 1.1 Pure and Mixed States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Density Matrices and Operators . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Density Matrices for Pure and Mixed States . . . . . . . . . . . . . . 7 1.2.2 Density Operator in Thermal Equilibrium . . . . . . . . . . . . . . . 8 1.3 Statistical Expectation Values of Operators...
متن کامل