Generation of Large-Amplitude Coherent-State Superposition via Ancilla-Assisted Photon Subtraction

Takahashi, Hiroki; Wakui, Kentaro; Suzuki, Setsuo; Takeoka, Masahiro; Hayasaka, Kazuhiro; Furusawa, Akira; Sasaki, Masahide

doi:10.1103/physrevlett.101.233605

Cited by 248 publications

(211 citation statements)

References 19 publications

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“…(23). In particular, we see that all number states |n are included in this set for specific values of g corresponding to the upper bound of Eq.…”

mentioning

confidence: 99%

“…Non-Gaussian states of light can now be handled in the laboratory [20][21][22][23][24][25] and have been proven essential in the field of continuous-variable quantum information [26][27][28][29][30], but they remain hard to classify. Identifying states of minimum uncertainty among them may lead to a better understanding of the structure of the state space in infinite dimension and, since the Heisenberg principle is at the heart of the limitations on measurement precision [31], to further developments in quantum metrology.…”

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confidence: 99%

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Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator

Mandilara¹,

Cerf

2012

Phys. Rev. A

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We rederive the Schrödinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to the harmonic oscillator, which can then be further exploited to find a larger class of constrained uncertainty relations. We derive an uncertainty relation under the constraint of a fixed degree of Gaussianity and prove that, remarkably, it is saturated by all eigenstates of the harmonic oscillator. This goes beyond the common knowledge that the (Gaussian) ground state of the harmonic oscillator saturates the uncertainty relation. The Heisenberg uncertainty principle [1] captures the difference between classical and quantum states, and sets a limit on the precision of incompatible quantum measurements. It has been introduced in the early days of quantum mechanics, but its form has evolved with the understanding and formulation of quantum physics throughout the years. The first rigorous mathematical proof of Heisenberg's uncertainty relation for the canonical operators of positionx and momentump [7] for more details), while the properties of the states saturating this inequality were also progressively unveiled. The original uncertainty relation (1) only concerned the operatorsx andp, but it was generalized to any pair of Hermitian operators by Schrödinger [8] and Robertson [9], in the case of pure states. In the same works, the anticommutator ofx andp was also included in Eq. (1), yielding a stronger uncertainty relation, (1) and (2) inx andp and the fact that we deal with the quadratic Hamiltonian of a harmonic oscillator. Then, we move on to find bounded uncertainty relations [15], which give stronger bounds than Eq. (2) for states on which some a priori information is known, such as their purity [7] or entropy [16]. Specifically, we derive a Gaussianity-bounded uncertainty relation, depending on the degree of Gaussianity of the state as measured by a parameter g that we introduce. We identify its corresponding set of MSs and find among them all the eigenstates of the harmonic oscillator. This yields a fundamental set of non-Gaussian minimum-uncertainty states, going beyond the common knowledge on the Heisenberg principle.Although the uncertainty relations, being at the root of quantum mechanics, have been investigated in various situations, such as multidimensional [17,18] or mixed states [7,16,19], our results imply that there is more to gain by analyzing them under the perspective of the Gaussian character of a state. Non-Gaussian states of light can now be handled in the laboratory [20][21][22][23][24][25] and have been proven essential in the field of continuous-variable quantum information [26][27][28][29][30], but they remain hard to classify. Identifying states of minimum uncertainty among them may lead to a better understanding of the structure of the state space in infinite dimension and, since the Heisenberg principle is at the heart of the limitations on measurement...

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“…(23). In particular, we see that all number states |n are included in this set for specific values of g corresponding to the upper bound of Eq.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator

Mandilara¹,

Cerf

2012

Phys. Rev. A

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“…The photonadded coherent state was implemented in the laboratory [23]. To generate the odd coherent state was proposed in some ways [41,[45][46][47], and implemented in other ways [48][49][50][51][52][53][54]. Applying local photon subtraction operations on the non-Gaussian entangled state, we can simply obtain the following form,…”

Section: Generation Of Non-gaussian Entangled Statesmentioning

confidence: 99%

Increasing and decreasing entanglement characteristics for continuous variables by a local photon subtraction

Lee

2013

Phys. Rev. A

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We investigate how the entanglement characteristics of a non-Gaussian entangled state are increased or decreased by a local photon subtraction operation. The non-Gaussian entangled state is generated by injecting a single-mode non-Gaussian state and a vacuum state into a 50:50 beam splitter. We consider a photon-added coherent stateâ † |α and an odd coherent state |α − | − α as a single-mode non-Gaussian state. In the regime of small |α|, we show that the performance of quantum teleportation and the second-order Einstein-Podolsky-Rosen-type correlation can both be enhanced, whereas the degree of entanglement decreases, for the output state when a local photon subtraction operation is applied to the non-Gaussian entangled state. The counterintuitive effect is more prominent in the limit of |α| ∼ 0.

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“…In this paper, we develop a theoretical time-domain description of the modefiltering process, and then experimentally demonstrate the successful mode-reshaping as predicted from the theory. The simple technique demonstrated here can be straightforwardly applied to various photon-subtraction protocols, including state-generation [10,11] and entanglement distillation [8].…”

Section: Introductionmentioning

confidence: 99%

Quantum mode filtering of non-Gaussian states for teleportation-based quantum information processing

et al. 2012

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We propose and demonstrate an effective mode-filtering technique of non-Gaussian states generated by photon-subtraction. More robust non-Gaussian states have been obtained by removing noisy low frequencies from the original mode spectrum. We show that non-Gaussian states preserve their non-classicality after quantum teleportation to a higher degree, when they have been modefiltered. This is indicated by a stronger negativity −0.033 ± 0.005 of the Wigner function at the origin, compared to −0.018 ± 0.007 for states that have not been mode-filtered. This technique can be straightforwardly applied to various kinds of photon-subtraction protocols, and can be a key ingredient in a variety of applications of non-Gaussian states, especially teleportation-based protocols towards universal quantum information processing.

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Generation of Large-Amplitude Coherent-State Superposition via Ancilla-Assisted Photon Subtraction

Cited by 248 publications

References 19 publications

Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator

Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator

Increasing and decreasing entanglement characteristics for continuous variables by a local photon subtraction

Quantum mode filtering of non-Gaussian states for teleportation-based quantum information processing

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