We propose a definition of nonclassicality for a single-mode quantum-optical process based on its action on coherent states. If a quantum process transforms a coherent state to a nonclassical state, it is verified to be nonclassical. To identify nonclassical processes, we introduce a representation for quantum processes, called the process-nonclassicality quasiprobability distribution, whose negativities indicate nonclassicality of the process. Using this distribution, we derive a relation for predicting nonclassicality of the output states for a given input state. We experimentally demonstrate our method by considering the single-photon addition as a nonclassical process and predicting nonclassicality of the output state for an input thermal state.We propose a definition of nonclassicality for a single-mode quantum-optical process based on its action on coherent states. If a quantum process transforms a coherent state to a nonclassical state, it is verified to be nonclassical. To identify nonclassical processes, we introduce a representation for quantum processes, called the process-nonclassicality quasiprobability distribution, whose negativities indicate nonclassicality of the process. Using this distribution, we derive a relation for predicting nonclassicality of the output states for a given input state. We experimentally demonstrate our method by considering the single-photon addition as a nonclassical process and predicting nonclassicality of the output state for an input thermal state.

arXiv:1302.0934Physical Review LettersApr 19, 201341 citations

Quantum Processes

Henry Pierce Stapp

Process StudiesJan 1, 20050 citations

Unitary quantum process tomography with unreliable pure input states

François Verdeil, Yannick Deville

Quantum process tomography (QPT) methods aim at identifying a given quantum process. QPT is a major quantum information processing tool, since it allows one to characterize the actual behavior of quantum gates, which are the building blocks of quantum computers. The present paper focuses on the estimation of a unitary process. This class is of particular interest because quantum mechanics postulates that the evolution of any closed quantum system is described by a unitary transformation. The standard approach of QPT is to measure copies of a particular set of predetermined (generally pure) states after they have been modified by the process to be identified. The main problem with this setup is that preparing an input state and setting it precisely to a predetermined value is challenging and thus yields errors. These errors can be decomposed into a sum of centered errors (i.e., whose average on all the copies is zero) and systematic errors that are the same for all the copies. The latter is often the main source of error in QPT. The algorithm we introduce works for any input states that make QPT theoretically possible (i.e., unless there are several solutions due to, e.g., a lack of diversity in the input states). The fact that we do not require the input states to be precisely set to predetermined values means that we can use a trick to remove the issue of systematic errors by considering that some states' copies are unknown but measured before they go through the process to be identified. We achieve this by splitting the copies of each input state into several groups and measuring the copies of the $k\mathrm{th}$ group after they have successively been transferred through $k$ instances of the process to be identified (each copy of each input state is used for only a single measurement). Using this approach, we can compute estimates of the measured states before and after they go through the process without using the knowledge we might have about the initial states. We test our algorithm with simulated data, and we assess its performance with a cnot gate on a trapped-ions qubit quantum computer.Quantum process tomography (QPT) methods aim at identifying a given quantum process. QPT is a major quantum information processing tool, since it allows one to characterize the actual behavior of quantum gates, which are the building blocks of quantum computers. The present paper focuses on the estimation of a unitary process. This class is of particular interest because quantum mechanics postulates that the evolution of any closed quantum system is described by a unitary transformation. The standard approach of QPT is to measure copies of a particular set of predetermined (generally pure) states after they have been modified by the process to be identified. The main problem with this setup is that preparing an input state and setting it precisely to a predetermined value is challenging and thus yields errors. These errors can be decomposed into a sum of centered errors (i.e., whose average on all the copies is zero) and systematic errors that are the same for all the copies. The latter is often the main source of error in QPT. The algorithm we introduce works for any input states that make QPT theoretically possible (i.e., unless there are several solutions due to, e.g., a lack of diversity in the input states). The fact that we do not require the input states to be precisely set to predetermined values means that we can use a trick to remove the issue of systematic errors by considering that some states' copies are unknown but measured before they go through the process to be identified. We achieve this by splitting the copies of each input state into several groups and measuring the copies of the $k\mathrm{th}$ group after they have successively been transferred through $k$ instances of the process to be identified (each copy of each input state is used for only a single measurement). Using this approach, we can compute estimates of the measured states before and after they go through the process without using the knowledge we might have about the initial states. We test our algorithm with simulated data, and we assess its performance with a cnot gate on a trapped-ions qubit quantum computer.

arXiv:2306.07867Physical Review ADec 11, 20232 citations

Quantum Processes

Bob Coecke, Aleks Kissinger

Cambridge University Press eBooksMar 16, 20170 citations

Quantum Processes

Wolfram Schommers

Jul 13, 201116 citations

The unitary dynamical state-locking process, the HSSS quantum search process, and the quantum-computing speedup theory

Xijia Miao

A unitary dynamical state-locking (UNIDYSLOCK) process is a unitary process that can transform two orthogonal states to two non-orthogonal states. Its inverse process, i.e., the QUANSDAM process could realize an exponential QC speedup in solving an unstructured search problem in the quantum-computing (QC) speedup theory (X. Miao, arXiv:1105.3573 [quant-ph] (2011)). In this paper the principle of how a UNIDYSLOCK process works is described on the basis of the QC speedup theory. A UNIDYSLOCK process does not exist at all in pure quantum mechanics. That it can change the quantum-state difference is original from the fundamental interaction between the quantum physical laws (i.e., the unitary quantum dynamics and the Hilbert-space symmetric structure) and the mathematical-logical principle of the search problem. It is characteristic for the QC speedup theory. Even if a usual quantum computational (Qc) process that is reversible or unitary contained a UNIDYSLOCK (or QUANSDAM) process, the contribution of the UNIDYSLOCK (or QUANSDAM) process to the QC speedup of the usual Qc process would be secondary or negligible. Whether or not a UNIDYSLOCK (or QUANSDAM) process can make an essential contribution to a QC speedup can distinguish the QC speedup theory from any usual Qc theory. In the paper the QC speedup mechanism of the HSSS quantum search process is also studied. The search process is essentially different from a usual quantum search algorithm. It works in both the usual Hilbert space and the math Hilbert space. Due to the math Hilbert space a mathematical-parallel operation is characteristic for the QC speedup theory, while a quantum-parallel operation is characteristic for the usual Qc theory. The fundamental interaction mentioned above and the fundamental quantum-computing resource play the main role in speeding up the search process.A unitary dynamical state-locking (UNIDYSLOCK) process is a unitary process that can transform two orthogonal states to two non-orthogonal states. Its inverse process, i.e., the QUANSDAM process could realize an exponential QC speedup in solving an unstructured search problem in the quantum-computing (QC) speedup theory (X. Miao, arXiv:1105.3573 [quant-ph] (2011)). In this paper the principle of how a UNIDYSLOCK process works is described on the basis of the QC speedup theory. A UNIDYSLOCK process does not exist at all in pure quantum mechanics. That it can change the quantum-state difference is original from the fundamental interaction between the quantum physical laws (i.e., the unitary quantum dynamics and the Hilbert-space symmetric structure) and the mathematical-logical principle of the search problem. It is characteristic for the QC speedup theory. Even if a usual quantum computational (Qc) process that is reversible or unitary contained a UNIDYSLOCK (or QUANSDAM) process, the contribution of the UNIDYSLOCK (or QUANSDAM) process to the QC speedup of the usual Qc process would be secondary or negligible. Whether or not a UNIDYSLOCK (or QUANSDAM) process can make an essential contribution to a QC speedup can distinguish the QC speedup theory from any usual Qc theory. In the paper the QC speedup mechanism of the HSSS quantum search process is also studied. The search process is essentially different from a usual quantum search algorithm. It works in both the usual Hilbert space and the math Hilbert space. Due to the math Hilbert space a mathematical-parallel operation is characteristic for the QC speedup theory, while a quantum-parallel operation is characteristic for the usual Qc theory. The fundamental interaction mentioned above and the fundamental quantum-computing resource play the main role in speeding up the search process.

arXiv:1612.05969Dec 18, 20160 citations

k\mathrm{th}

group after they have successively been transferred through

k

instances of the process to be identified (each copy of each input state is used for only a single measurement). Using this approach, we can compute estimates of the measured states before and after they go through the process without using the knowledge we might have about the initial states. We test our algorithm with simulated data, and we assess its performance with a cnot gate on a trapped-ions qubit quantum computer.