Input Coherent State Research Articles

Frequency conversion of continuous variable quantum states

The frequency conversion of cw continuous variable quantum states via second-order nonlinear optical processes is theoretically analyzed. It is shown that wideband frequency conversion of cw continuous variable quantum states is feasible by sum-frequency generation. For difference-frequency generation, besides as an optimal-phase-conjugation frequency-conversion process, any one quadrature of the quantum state can be frequency converted through it. Particularly, we analyze the influence of pump field fluctuations on the fidelity of the frequency-conversion process for a coherent state input.

Demonstration of deterministic and high fidelity squeezing of quantum information

By employing at recent proposal (R. Filip, P. Marek and U.L. Andersen, Phys. Rev. A {\bf 71}, 042308 (2005) \cite{Filip05.pra}), we experimentally demonstrate a universal, deterministic and high-fidelity squeezing transformation of an optical field. It relies only on linear optics, homodyne detection, feedforward and an ancillary squeezed vacuum state, thus direct interaction between a strong pump and the quantum state is circumvented. We demonstrate three different squeezing levels for a coherent state input. This scheme is highly suitable for the fault-tolerant squeezing transformation in a continuous variable quantum computer.

Classical capacity of bosonic broadcast communication and a minimum output entropy conjecture

Previous work on the classical information capacities of bosonic channels has established the capacity of the single-user pure-loss channel, bounded the capacity of the single-user thermal-noise channel, and bounded the capacity region of the multiple-access channel. The latter is a multiple-user scenario in which several transmitters seek to simultaneously and independently communicate to a single receiver. We study the capacity region of the bosonic broadcast channel, in which a single transmitter seeks to simultaneously and independently communicate to two different receivers. It is known that the tightest available lower bound on the capacity of the single-user thermal-noise channel is that channel's capacity if, as conjectured, the minimum von Neumann entropy at the output of a bosonic channel with additive thermal noise occurs for coherent-state inputs. Evidence in support of this minimum output entropy conjecture has been accumulated, but a rigorous proof has not been obtained. We propose a minimum output entropy conjecture that, if proved to be correct, will establish that the capacity region of the bosonic broadcast channel equals the inner bound achieved using a coherent-state encoding and optimum detection. We provide some evidence that supports this conjecture, but again a full proof is not available.

Realistic teleportation of coherent states using squeezed vacuum states

This paper presents a realistic scheme for the teleportation of coherent states in which a two-mode squeezed vacuum state serves as the quantum channel and the position-sum and momentum-difference of two local modes serve as the measuring observables. The average fidelity of the teleportation of coherent states is derived for finite squeezing parameters and it turns out that fidelity greater than ½ cannot be achieved by using a classical channel alone and the probability distribution of the measurement result is a Gaussian distribution around the unknown parameter of the input coherent state with a width given by the squeezing parameter.

Continuous-variable quantum teleportation with non-Gaussian resources

We investigate continuous variable quantum teleportation using non-Gaussian states of the radiation field as entangled resources. We compare the performance of different classes of degaussified resources, including two-mode photon-added and two-mode photon-subtracted squeezed states. We then introduce a class of two-mode squeezed Bell-like states with one-parameter dependence for optimization. These states interpolate between and include as subcases different classes of degaussified resources. We show that optimized squeezed Bell-like resources yield a remarkable improvement in the fidelity of teleportation both for coherent and nonclassical input states. The investigation reveals that the optimal non-Gaussian resources for continuous variable teleportation are those that most closely realize the simultaneous maximization of the content of entanglement, the degree of affinity with the two-mode squeezed vacuum, and the, suitably measured, amount of non-Gaussianity.

Proposal for generating Fock states in traveling wave fields

Abstract We describe a proposal for the generation of a single-mode photonic number state, | N 〉 , in a traveling wave optical field. The state is obtained by state reduction from an input coherent state using Kerr media. Our method is based on a previous scheme used for hole burning in the Fock space by minimizing the Mandel Q parameter. The same method was used by Maia et al., but ours is different, it requires only one single photon injected in the entire setup and one photon detection at the end.

Conditional quantum-state engineering using ancillary squeezed-vacuum states

We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection, and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock state of n <= 4, and conjecture that this can be generalized for an arbitrary n Fock state. We describe our experimental demonstration of this scheme using coherent input states and measuring experimental fidelities that are only achievable using quantum resources.

Optimal estimation of squeezing

We present the optimal estimation of an unknown squeezing transformation of the radiation field. The optimal estimation is unbiased and is obtained by properly considering the degeneracy of the squeezing operator. For coherent input states, the root-mean square of the estimation scales as ${(2\sqrt{\overline{n}})}^{\ensuremath{-}1}$ versus the average photon number $\overline{n}$, while it can be improved to ${(2\overline{n})}^{\ensuremath{-}1}$ by using displaced squeezed states.

Non-orthogonal positive operator valued measure phase distributions of one- and two-mode electromagnetic fields

Non-orthogonal positive operator valued measure (POVM) phase distributions are analysed for one-mode and two-mode electromagnetic (em) waves. For a one-mode em field the non-orthogonal POVM phase distribution is given indirectly from the one-mode density matrix which is obtained by measurements of the quadrature probability distribution and a certain integration based on sampling pattern functions. The compensation for non-unitary detection is demonstrated by making explicit calculations for coherent states. For a two-mode em field the non-orthogonal POVM relative phase distribution is related to an angular momentum basis and two-mode angular momentum phase states. We compare our analysis with two-mode phase measurements made by other authors. We demonstrate the use of the present methods by analysing the phase distribution for the em field output from a Mach?Zehnder interferometer. For the case of coherent state input the phase distribution is obtained using the one-mode non-orthogonal POVM method, since in this case we get two coherent state outputs which are not correlated. For the case of a number state input the phase distribution is analysed by the two-mode non-orthogonal POVM method as there are strong correlations between the two em wave outputs.

MINIMUM OUTPUT ENTROPY OF A GAUSSIAN BOSONIC CHANNEL

The entropy at the output of a Bosonic channel is analyzed when coherent fields are randomly added to the signal. Coherent-state inputs are conjectured to provide the minimum output entropy. Supporting physical and mathematical evidence is provided.

NONLINEAR OPTICAL PROCESSES PRODUCING THREE-FOLD ENTANGLEMENTS VIA χ(2) AND χ(3) MATERIAL

It is demonstrated that three-fold entangled states could lead to photon duplication as well as measurement of photon numbers of the first kind. Nonlinear optical schemes using χ(2) and χ(3) material for realizing such systems are suggested. Weak input power signals and fast response photodetectors are required for ideal operations. A criterion of incorrect operation of photon number cloning is also introduced and the operations of these realizations are studied for high-speed photodetectors and coherent state input field.

Linear optical extraction of photon-number Fock states from coherent states

Photon-number Fock states play important roles in quantum optics. However, the generation of the states are very difficult because of the lack of large effective nonlinearities. In this Rapid Communication, I show a scheme to produce the Fock state from an input coherent state by using only linear optics method and projection measurements. I analyze the case of five-photon number state generation from coherent states for a specific case of the scheme. It is possible to remove the vacuum state from the output state when one introduces quantum nondemolition measurement that can also be implemented with all linear optics setup.

Minimum output entropy of bosonic channels: A conjecture

The von Neumann entropy at the output of a bosonic channel with thermal noise is analyzed. Coherent-state inputs are conjectured to minimize this output entropy. Physical and mathematical evidence in support of the conjecture is provided. A stronger conjecture--that output states resulting from coherent-state inputs majorize the output states from other inputs--is also discussed.

Retrodictive quantum optical state engineering

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.

Quantum teleportation of light beams

We experimentally demonstrate quantum teleportation for continuous variables using squeezed-state entanglement. The teleportation fidelity for a real experimental system is calculated explicitly, including relevant imperfection factors such as propagation losses, detection inefficiencies and phase fluctuations. The inferred fidelity for input coherent states is F = 0.61 +- 0.02, which when corrected for the efficiency of detection by the output observer, gives a fidelity of 0.62. By contrast, the projected result based on the independently measured entanglement and efficiencies is 0.69. The teleportation protocol is explained in detail, including a discussion of discrepancy between experiment and theory, as well as of the limitations of the current apparatus.

Nonlinear interferometer as a resource for maximally entangled photonic states: Application to interferometry

Nonlinear interferometers are Mach-Zehnder interferometers with Kerr media in either one or both arms. We refer to these devices, respectively, as the asymmetric and symmetric nonlinear interferometers. In the asymmetric case, with one input mode in the vacuum, it is possible to generate maximally entangled photonic states or superpositions of such states. We consider the device as a resource of entangled states for applications to Heisenberg-limited interferometry. Interferometry with the maximally entangled states cannot be performed by simply subtracting the output photocounts as in standard interferometry. Instead, one must perform parity measurements on only one of the output beams. We show that the symmetric nonlinear interferometer, with one input mode in the vacuum, may be used to perform such parity measurements. The same device is shown to produce, with an input coherent state and upon projective measurements, even or odd coherent states, examples of the Schr\odinger-cat states.

Telecloning of continuous quantum variables.

We propose entangled (M+1)-mode quantum states as a multiuser quantum channel for continuous-variable communication. Arbitrary quantum states can be sent via this channel simultaneously to M remote and separated locations with equal minimum excess noise in each output mode. For a set of coherent-state inputs, the channel realizes optimal symmetric 1-->M cloning at a distance ("telecloning"). It also provides the optimal cloning of coherent states without the need of amplifying the state of interest. The generation of the multiuser quantum channel requires no more than two 10log10[(root square[M]-1)/(root square[M]+1)] dB squeezed states and M beam splitters.

Quantum-scissors device for optical state truncation: A proposal for practical realization

We propose a realizable experimental scheme to prepare superposition of the vacuum and one-photon states by truncating an input coherent state. The scheme is based on the quantum scissors device proposed by Pegg, Phillips, and Barnett [Phys. Rev. Lett. 81, 1604 (1998)] and uses photon-counting detectors, a single photon source, and linear optical elements. Realistic features of the photon counting and single-photon generation are taken into account and possible error sources are discussed together with their effect on the fidelity and efficiency of the truncation process. Wigner function and phase distribution of the generated states are given and discussed for the evaluation of the proposed scheme.

Measuring the phase variance of light

The results of experiments designed to measure the operational phase cosine and sine variances of weak states of light disagree with the variances predicted by canonical phase formalisms. As these variances are fundamental manifestations of the quantum nature of phase, it is important to be able to measure the canonical variances also. A recent suggestion to do so, based on the use of a two-component probe, involves the difficult preparation of exotic states of light which have not yet been produced. In this paper we show how the variances can be measured with simple coherent state inputs. The retrodictive formalism of quantum mechanics provides useful insight into the physics involved.

Quantum phase properties of impeded second-harmonic generation

Using the statistical characteristics of the photon number, quantum phase and field quadratures, based on the preferred phase, we have demonstrated a Kerr-like behaviour for the cascaded second-order nonlinearities and have studied thoroughly the oscillations superimposed on the Kerr-like trend for an input coherent state. We have performed a global study over the entire quantum period in an idealized model of the trend of this process based on the lossless Kerr progression.