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Physical Review A

Optical state truncation

Stephen Mark Barnett, David Thomas Pegg

Published Dec 1, 1999• 53 citations
Publisher

Abstract

We investigate the effects of photodetector imperfections on a recently proposed device designed to truncate physically a state of light. We find that the mixed state produced in the presence of the imperfections has a surprisingly good fidelity with the required state. For convenience and mathematical simplicity, we make use of the quantum-mechanical retrodictive formalism but show that the results are equivalent to those obtainable from more usual predictive formalism.

DOI
10.1103/physreva.60.4965

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We investigate the effects of photodetector imperfections on a recently proposed device designed to truncate physically a state of light. We find that the mixed state produced in the presence of the imperfections has a surprisingly good fidelity with the required state. For convenience and mathematical simplicity, we make use of the quantum-mechanical retrodictive formalism but show that the results are equivalent to those obtainable from more usual predictive formalism.
The usual formalism of quantum mechanics is predictive with state vectors being assigned on the basis of past preparation procedures. The retrodictive formalism, in which some state vectors are assigned on the basis of future measurement results is less usual, although it has been known for some time. Although at first sight this formalism may appear to be anticausal and subject to paradoxes, if used carefully it still predicts the same measurable correlations as the more usual approach despite different assignments of state vectors to states in the interval between preparation and measurement of the system. Here we use a procedure which involves retrodiction to examine some quantum optical processes, including a recent state truncation process. The collapse of the state vector occurs at a different time from that for the usual approach underlining the difficulty in regarding the collapse as a real physical process.
Although it has been known for some time that quantum mechanics can be formulated in a way that treats prediction and retrodiction on an equal footing, most attention in engineering quantum states has been devoted to predictive states, that is, states associated with the a preparation event. Retrodictive states, which are associated with a measurement event and propagate backwards in time, are also useful, however. In this paper we show how any retrodictive state of light that can be written to a good approximation as a finite superposition of photon number states can be generated by an optical multiport device. The composition of the state is adjusted by controlling predictive coherent input states. We show how the probability of successful state generation can be optimised by adjusting the multiport device and also examine a versatile configuration that is useful for generating a range of states.
Although it has been known for some time that quantum mechanics can be formulated in a way that treats prediction and retrodiction on an equal footing, most attention in engineering quantum states has been devoted to predictive states, that is, states associated with a preparation event. Retrodictive states, which are associated with a measurement event and propagate backwards in time, are also useful, however. In this paper it is shown how any retrodictive state of light that can be written to a good approximation as a finite superposition of photon number states can be generated by an optical multiport device. The composition of the state is adjusted by controlling predictive coherent input states. It is shown how the probability of successful state generation can be optimized by adjusting the multiport device and also a versatile configuration that is useful for generating a range of states is examined.
Although it has been known for some time that quantum mechanics can be formulated in a way that treats prediction and retrodiction on an equal footing, most attention in engineering quantum states has been devoted to predictive states, that is, states associated with a preparation event. Retrodictive states, which are associated with a measurement event and propagate backwards in time, are also useful, however. In this paper it is shown how any retrodictive state of light that can be written to a good approximation as a finite superposition of photon number states can be generated by an optical multiport device. The composition of the state is adjusted by controlling predictive coherent input states. It is shown how the probability of successful state generation can be optimized by adjusting the multiport device and also a versatile configuration that is useful for generating a range of states is examined.
A possible way of generating nonclassical states of light is via the truncation of a given state in the Fock basis. In recent work, we presented an alternative scheme for such quantum scissors [ Phys. Rev. A 104 , 033715 ( 2021 ) PLRAAN 1050-2947 10.1103/PhysRevA.104.033715 ], employing a nondegenerate parametric amplifier, a beam splitter, and photodetectors. An advantage of this setup is that it does not require the generation of Fock states beforehand, as in previous proposals. Here we extend this treatment to mixed input states. We show the possibilities of generating truncated states with either a maximum Fock number N or states having a minimum Fock number N . We discuss two specific examples of states to be truncated: (i) the thermal state and (ii) the phase-diffused coherent state. In either case, the generated field states can present sub-Poissonian statistics as well as non-Gaussian character. These nonclassical properties can be adjusted by changing the parameters of the scissors, e.g., the amplifier strength and the beam-splitter transmittance.
We present a scheme of quantum state truncation in the Fock basis (quantum scissors), based on the combined action of a nondegenerate optical parametric amplifier and a beam splitter. Differently from previously proposed linear-optics-based quantum scissors devices, which depend on reliable Fock state sources, our scheme requires only readily available Gaussian states, such as coherent state inputs (vacuum state included). A truncated state is generated after performing photodetections in the global state. We find that, depending on which output ports each of the two photodetectors is positioned, different types of truncated states may be produced: (i) states having a maximum Fock number of NNN, or (ii) states having a minimum Fock number NNN. In order to illustrate our method, we discuss an example having as input states a coherent state in the beam splitter and vacuum states in the amplifier, and show that the resulting truncated states display nonclassical properties, such as sub-Poissonian statistics and squeezing. We quantify the nonclassicality degree of the generated states using the Wigner-Yanase skew information measure. For complementarity, we discuss the efficiency of the protocol, e.g., generation probability as well as the effects of imperfections such as the detector's quantum efficiency and dark counts rate.