Quantum electronics is significantly involved in the development of the field of quantum information processing. In this domain, the growth of Blind Quantum Source Separation and Blind Quantum Process Tomography has led, within the formalism of the Hilbert space, to the introduction of the concept of a Random-Coefficient Pure State, or RCPS: the coefficients of its development in the chosen basis are random variables. This paper first describes an experimental situation necessitating its introduction. While the von Neumann approach to a statistical mixture considers statistical properties of an observable, in the presence of an RCPS one has to manipulate statistical properties of probabilities of measurement outcomes, these probabilities then being themselves random variables. It is recalled that, in the presence of a von Neumann statistical mixture, the consistency of the density operator \r{ho} formalism is based on a postulate. The interest of the RCPS concept is presented in the simple case of a spin 1/2, through two instances. The most frequent use of the \r{ho} formalism by users of quantum mechanics is a motivation for establishing some links between a given RCPS and the language of the density operator formalism, while keeping in mind that the situation described by an RCPS is different from the one which has led to the introduction of \r{ho}. It is established that the Landau - Feynman use of \r{ho} is mobilized in a situation differing from both the von Neumann statistical mixture and the RCPS. It is shown that the use of the higher-order moments of a well-chosen random variable helps solving a problem already identified by Zeh in 1970.Quantum electronics is significantly involved in the development of the field of quantum information processing. In this domain, the growth of Blind Quantum Source Separation and Blind Quantum Process Tomography has led, within the formalism of the Hilbert space, to the introduction of the concept of a Random-Coefficient Pure State, or RCPS: the coefficients of its development in the chosen basis are random variables. This paper first describes an experimental situation necessitating its introduction. While the von Neumann approach to a statistical mixture considers statistical properties of an observable, in the presence of an RCPS one has to manipulate statistical properties of probabilities of measurement outcomes, these probabilities then being themselves random variables. It is recalled that, in the presence of a von Neumann statistical mixture, the consistency of the density operator \r{ho} formalism is based on a postulate. The interest of the RCPS concept is presented in the simple case of a spin 1/2, through two instances. The most frequent use of the \r{ho} formalism by users of quantum mechanics is a motivation for establishing some links between a given RCPS and the language of the density operator formalism, while keeping in mind that the situation described by an RCPS is different from the one which has led to the introduction of \r{ho}. It is established that the Landau - Feynman use of \r{ho} is mobilized in a situation differing from both the von Neumann statistical mixture and the RCPS. It is shown that the use of the higher-order moments of a well-chosen random variable helps solving a problem already identified by Zeh in 1970.

arXiv:2201.03248Jan 10, 20221 citation

Pseudo-Random Operators for Quantum Information Processing: Theory and Applications

Joseph Emerson

Bulletin of the American Physical SocietyMar 24, 20050 citations

Bipartite entanglement of large quantum systems

Antonella De Pasquale

In this thesis we study the behavior of bipartite entanglement of a large quantum system, by analyzing the distribution of the Schmidt coefficients of the reduced density matrix. Applying the general methods of classical statistical mechanics, we develop a canonical approach for the study of the distribution of these coefficients for a fixed value of the average entanglement. We introduce a partition function depending on a fictitious temperature, which localizes the measure on the set of states with higher and lower entanglement, if compared to typical (random) states with respect to the Haar measure. The purity of one subsystem, which is our entanglement measure/indicator, plays the role of energy in the partition function. This thesis consists of two parts. In the first part, we completely characterize the distribution of the purity and of the eigenvalues for pure states. The global picture unveils several locally stable solutions exchange stabilities, through the presence of first and second order phase transitions. We also detect the presence of metastable states. In the second part, we focus on mixed states. Through the same statistical approach, we determine the exact expression of the first two moments of the local purity and the high temperature expansion of the first moment. We also bridge our problem with the theory of quantum channels, more precisely we exploit the symmetry properties of the twirling transformations in order to compute the exact expression for the first moment of the local purity.In this thesis we study the behavior of bipartite entanglement of a large quantum system, by analyzing the distribution of the Schmidt coefficients of the reduced density matrix. Applying the general methods of classical statistical mechanics, we develop a canonical approach for the study of the distribution of these coefficients for a fixed value of the average entanglement. We introduce a partition function depending on a fictitious temperature, which localizes the measure on the set of states with higher and lower entanglement, if compared to typical (random) states with respect to the Haar measure. The purity of one subsystem, which is our entanglement measure/indicator, plays the role of energy in the partition function. This thesis consists of two parts. In the first part, we completely characterize the distribution of the purity and of the eigenvalues for pure states. The global picture unveils several locally stable solutions exchange stabilities, through the presence of first and second order phase transitions. We also detect the presence of metastable states. In the second part, we focus on mixed states. Through the same statistical approach, we determine the exact expression of the first two moments of the local purity and the high temperature expansion of the first moment. We also bridge our problem with the theory of quantum channels, more precisely we exploit the symmetry properties of the twirling transformations in order to compute the exact expression for the first moment of the local purity.

arXiv:1206.6749Jun 28, 20125 citations

Beyond Single-Copy Quantum Measurements: Ensemble Structure Enables Basis Discrimination

Amitava Datta

Abstract A central tenet of quantum theory is that ensembles sharing the same density matrix are indistinguishable under measurements on individual systems. We show that this indistinguishability can break down when additional structure is present across multiple copies. We investigate ensembles of qubits prepared in either the computational ( $Z$ ) or Hadamard ( $X$ ) basis under a same-basis constraint. All qubits within a batch are prepared in the same basis, but with randomly distributed outcomes such that the reduced state of each individual qubit is maximally mixed. We introduce an experimentally realizable protocol that exploits multi-copy statistical structure to distinguish these ensembles. The graph-state protocol identifies the two basis through stabilizer measurements and higher-order statistical features. Our protocol has been implemented on the \texttt{ibm\_fez} superconducting quantum processor and demonstrates robust performance in the presence of realistic noise, achieving near-unity classification accuracy as the number of samples increases. While single-copy measurements are uninformative, aggregating outcomes across multiple instances produces a clear and scalable separation between basis families. Our result identifies a regime in which quantum information is not accessible at the level of individual systems but emerges through structured multi-copy measurements. This highlights the role of higher-order statistical correlations in quantum information processing and provides a practical route for exploiting such structure on near-term quantum devices.Abstract A central tenet of quantum theory is that ensembles sharing the same density matrix are indistinguishable under measurements on individual systems. We show that this indistinguishability can break down when additional structure is present across multiple copies. We investigate ensembles of qubits prepared in either the computational ($Z$) or Hadamard ($X$) basis under a same-basis constraint. All qubits within a batch are prepared in the same basis, but with randomly distributed outcomes such that the reduced state of each individual qubit is maximally mixed. We introduce an experimentally realizable protocol that exploits multi-copy statistical structure to distinguish these ensembles. The graph-state protocol identifies the two basis through stabilizer measurements and higher-order statistical features. Our protocol has been implemented on the \texttt{ibm\_fez} superconducting quantum processor and demonstrates robust performance in the presence of realistic noise, achieving near-unity classification accuracy as the number of samples increases. While single-copy measurements are uninformative, aggregating outcomes across multiple instances produces a clear and scalable separation between basis families. Our result identifies a regime in which quantum information is not accessible at the level of individual systems but emerges through structured multi-copy measurements. This highlights the role of higher-order statistical correlations in quantum information processing and provides a practical route for exploiting such structure on near-term quantum devices.

Jul 10, 20260 citations

Efficient Quantum Information Processing via Quantum Compressions

Yun Kai Deng, Ming‐Xing Luo, S. Y.

International Journal of Theoretical PhysicsApr 24, 20150 citations

Z

) or Hadamard (

X

) basis under a same-basis constraint. All qubits within a batch are prepared in the same basis, but with randomly distributed outcomes such that the reduced state of each individual qubit is maximally mixed. We introduce an experimentally realizable protocol that exploits multi-copy statistical structure to distinguish these ensembles. The graph-state protocol identifies the two basis through stabilizer measurements and higher-order statistical features. Our protocol has been implemented on the \texttt{ibm\_fez} superconducting quantum processor and demonstrates robust performance in the presence of realistic noise, achieving near-unity classification accuracy as the number of samples increases. While single-copy measurements are uninformative, aggregating outcomes across multiple instances produces a clear and scalable separation between basis families. Our result identifies a regime in which quantum information is not accessible at the level of individual systems but emerges through structured multi-copy measurements. This highlights the role of higher-order statistical correlations in quantum information processing and provides a practical route for exploiting such structure on near-term quantum devices.