Luis and Sánchez-Soto Reply:

Luis, Alfredo; Ll, Sánchez-Soto

doi:10.1103/physrevlett.84.2041

Cited by 66 publications

(130 citation statements)

References 5 publications

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“…This correlation, which is clear in the jn, m͘ basis, extends as well to any other basis. Because of this, the realization of a measurement on H s or H i reduces the state in the other Hilbert space to a state strongly related to the measurement performed and its outcome [8]. Since we are dealing with two simultaneous measurements, we can express the result obtained in two different but equivalent ways.…”

Section: (Received 22 December 1998)mentioning

confidence: 99%

Complete Characterization of Arbitrary Quantum Measurement Processes

1999

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We examine two simple and feasible practical schemes allowing the complete determination of any quantum measuring arrangement. This is illustrated with the example of parity measurement.PACS numbers: 03.65. Bz, 42.50.Ar, 42.50.Dv In the most standard picture of quantum mechanics the statistics of every measurement are governed by the projection of the system state on the orthogonal eigenstates of a set of commuting self-adjoint operators representing the measured observables. This implicitly assumes that the measurement is performed on a closed system.A more complete and realistic picture must encompass the possibility of controllable as well as unpredictable couplings of the observed system with external agents. This is to say that the measurement is performed, in general, on an open system. Among other consequences, this extends the idea of observables beyond self-adjoint operators, introducing generalized measurements described by positive operator measures (POMs).In particular, this occurs when a standard measurement is preceded by an interaction of the observed system with other degrees of freedom that are in a fixed and known initial state [1]. On the other hand, the process can also involve uncontrollable influences (usually undesired) of outer degrees of freedom. This is frequently the case with couplings with reservoirs and other mechanisms leading to losses and decoherence effects, for instance. In many practical situations it is not possible to predict which external variables are involved or the way they affect the performance of the measurement. In other words, to some extent, the real measurement differs from the intended one in an unpredictable way.In this paper we present two simple and feasible practical procedures that allow us to determine completely any quantum measurement process. The objective of such a characterization is to obtain in practice the actual POM governing the statistics. This would allow one to ascertain to what extent the planned performance is reached by revealing undesired deviations.The system, which is the object of the observation, and the external variables involved are described by the Hilbert spaces H s and H a , respectively. Since the total Hilbert space H H s ≠ H a represents by definition a closed system, the system-environment interaction can always be implemented by a unitary operator U acting on H . The system is initially in an arbitrary state with density matrix r s , while the external variables will be in some state r a that does not depend on r s . After the interaction, some set of compatible observables are measured on the output state Ur s r a U y . The statistics of the measurement are given by the projection on a set of orthonormal vectors jk͘ whose span need not coincide with H s :where P ͑k͒ is the probability of the outcome k. This is a standard ideal measurement because H s ≠ H a is a closed system. Since r a is fixed and does not depend on r s , the information provided by the measurement can be regarded as information about r s . This interpr...

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Section: (Received 22 December 1998)mentioning

confidence: 99%

Complete Characterization of Arbitrary Quantum Measurement Processes

1999

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“…We can now recast this POVM expressed in local properties in terms of the phase difference ϕ − ϕ A − ϕ B and sum ϕ + ϕ A + ϕ B , both of which are joint properties of the qubits. Moreover, to make the associated POVM 2π-periodic we define [24] Λ…”

Section: Joint Phase Properties Of Two Qubitsmentioning

confidence: 99%

Measurable entanglement criterion for two qubits

2003

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We propose a directly measurable criterion for the entanglement of two qubits. We compare the criterion with other criteria, and we find that for pure states, and some mixed states, it coincides with the state's concurrence. The measure can be obtained with a Bell state analyser and the ability to make general local unitary transformations. However, the procedure fails to measure the entanglement of a general mixed two-qubit state.

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“…Formula (3) suggests that this could be achieved by probing the quantum operation E with one part of the EPR state |Ψ . To make this continuous-variable ancilla-assisted quantum process tomography [9,10] experimentally feasible, the unphysical infinitely squeezed EPR state may be replaced with a two-mode squeezed vacuum with finite squeezing [3],…”

Section: Quantum Process Tomographymentioning

confidence: 99%

“…This is particularly relevant for continuous variable quantum process tomography [3,4,[27][28][29][30], which aims at characterization of quantum operations on modes of quantized electromagnetic fields. Here, the most natural and readily available probe states are represented by coherent states |α , and the output states can be conveniently measured with homodyne detectors [6,8].…”

Section: Introductionmentioning

confidence: 99%

“…Quantum operations and channels can be completely characterized by quantum process tomography [1][2][3][4][5], which represents an extension of quantum state tomography [6][7][8] to quantum operations. Typically, the quantum operation E is probed with a sufficient number of input states ρ j , measurements in several different bases are performed on the output states E(ρ j ), and the quantum operation is reconstructed from the experimental data.…”

Section: Introductionmentioning

confidence: 99%

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Continuous-variable quantum process tomography with squeezed-state probes

Fiurášek¹

2015

Phys. Rev. A

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We propose a procedure for tomographic characterization of continuous variable quantum operations which employs homodyne detection and single-mode squeezed probe states with a fixed degree of squeezing and anti-squeezing and a variable displacement and orientation of squeezing ellipse. Density matrix elements of a quantum process matrix in Fock basis can be estimated by averaging well behaved pattern functions over the homodyne data. We show that this approach can be straightforwardly extended to characterization of quantum measurement devices. The probe states can be mixed, which makes the proposed procedure feasible with current technology.

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Luis and Sánchez-Soto Reply:

Cited by 66 publications

References 5 publications

Complete Characterization of Arbitrary Quantum Measurement Processes

Complete Characterization of Arbitrary Quantum Measurement Processes

Measurable entanglement criterion for two qubits

Continuous-variable quantum process tomography with squeezed-state probes

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