Quantum Benchmark via an Uncertainty Product of Canonical Variables

2016

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We present quantum fidelity benchmarks for continuous-variable (CV) quantum devices to outperform quantum channels which can transmit at most k-dimensional coherences for positive integers k. We determine an upper bound of an average fidelity over Gaussian distributed coherent states for quantum channels whose Schmidt class is k. This settles fundamental fidelity steps where the known classical limit and quantum limit correspond to the two endpoints of k = 1 and k = ∞, respectively. It turns out that the average fidelity is useful to verify to what extent an experimental CV gate can transmit a high dimensional coherence. The result is further extended to be applicable to general quantum operations or stochastic quantum channels. While the fidelity is often associated with heterodyne measurements in quantum optics, we can also obtain similar criteria based on quadrature deviations determined via homodyne measurements.

“…Let E be a quantum operation. We define the meansquare deviations for canonical quadratures [27,39,40] asV…”

Section: A Canonical Quantum Noise and Fidelitymentioning

confidence: 99%

Schmidt-number benchmarks for continuous-variable quantum devices

2016

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“…Mathematically, it implies the Choi-Jamiolkowsky (CJ) state of the channel is entangled, hence, there exists, at least, one entangled input state whose inseparability maintains under the channel action. There have been several works to determine such classical fidelities [3][4][5][9][10][11] or other forms of EB limits [12,13]. One can also apply the notion of EB limits to quantum operations, namely, trace-non-increasing class of completely positive (CP) maps [14,15].…”

mentioning

confidence: 99%

“…In this report, we present a general method to convert a separable condition to an EB condition for continuousvariable quantum channels as a generalization of the method developed in [13]. Given a formula of entanglement witness we compose an EB condition by separately assigning an entangled density operator.…”

mentioning

confidence: 99%

“…It is well-known that the sum condition [26] and the product condition [28] are sufficient for witnessing two-mode Gaussian entanglement. By applying our method we can translate them into the EB conditions with the input ensemble of the Gaussian distributed coherent states in [13] (Corollary 1 and Proposition, respectively), which are sufficient to witness onemode Gaussian channels in the quantum domain, namely, one-mode Gaussian channels being nonmember of the EB class. Further, the formalism developed in Ref.…”

mentioning

confidence: 99%

“…Further, the formalism developed in Ref. [13] would be usable as a quantitative quantum benchmark because it can be related to entanglement of formation on the CJ state (See Ref. [29]).…”

mentioning

confidence: 99%

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Converting separable conditions to entanglement-breaking conditions

2016

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We present a general method to derive entanglement breaking (EB) conditions for continuousvariable quantum gates. We start with an arbitrary entanglement witness, and reach an EB condition. The resultant EB condition is applicable not only for quantum channels but also for general quantum operations, namely, trace-non-increasing class of completely positive maps. We illustrate our method associated with a quantum benchmark based on the input ensemble of Gaussian distributed coherent states. We also exploit our idea for channels acting on finite dimensional systems and present a Schmidt-number benchmark based on input states of two mutually unbiased bases and measurements of generalized Pauli operators.An important task for future realization of quantum information technology is to establish a reliable quantum channel. A powerful tool to estimate an experimental implementation of quantum gates is quantum process tomography. However, it is not always feasible to measure the input-and-output relations for a set of tomographic complete states. Instead of tomographic approach, one may be interested in probing a basic coherence of quantum channels using a small set of feasible input states. The quantum benchmarks provide such a method based on the context of quantum entanglement [1][2][3][4][5][6][7]. A quantum benchmark is typically determined by an upper bound of an average fidelity achieved by a class of quantum channels called entanglement breaking (EB) [8]. If an experimental fidelity surpasses the fidelity bound we can verify that any classical measure-and-prepare map is unable to simulate the channel. Mathematically, it implies the Choi-Jamiolkowsky (CJ) state of the channel is entangled, hence, there exists, at least, one entangled input state whose inseparability maintains under the channel action. There have been several works to determine such classical fidelities [3][4][5][9][10][11] or other forms of EB limits [12,13]. One can also apply the notion of EB limits to quantum operations, namely, trace-non-increasing class of completely positive (CP) maps [14,15]. In addition to a proof of the inseparability in the physical process, one can demonstrate a more specified type of channel's coherence by quantifying the amount of entanglement in the CJ state [16][17][18].Although it has been known that an EB condition is mathematically equivalent to a separable condition, the varieties of known EB conditions are rather limited compared with those of known separable conditions. In fact, one can easily find several systematic methods to produce a series of separable conditions [19][20][21] whereas potential applications of separable conditions to the quantum benchmark problems have little been mentioned in the literatures on the separability problems [22,23].In this report, we present a general method to convert a separable condition to an EB condition for continuousvariable quantum channels as a generalization of the method developed in [13]. Given a formula of entanglement witness we compose an EB condition by sepa...

Amplification uncertainty relation for probabilistic amplifiers

2015

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Traditionally, quantum amplification limit refers to the property of inevitable noise addition on canonical variables when the field amplitude of an unknown state is linearly transformed through a quantum channel. Recent theoretical studies have determined amplification limits for cases of probabilistic quantum channels or general quantum operations by specifying a set of input states or a state ensemble. However, it remains open how much excess noise on canonical variables is unavoidable and whether there exists a fundamental trade-off relation between the canonical pair in a general amplification process. In this paper we present an uncertainty-product form of amplification limits for general quantum operations by assuming an input ensemble of Gaussian distributed coherent states. It can be derived as a straightforward consequence of canonical uncertainty relations and retrieves basic properties of the traditional amplification limit. In addition, our amplification limit turns out to give a physical limitation on probabilistic reduction of an Einstein-Podolsky-Rosen uncertainty. In this regard, we find a condition that probabilistic amplifiers can be regarded as local filtering operations to distill entanglement. This condition establishes a clear benchmark to verify an advantage of non-Gaussian operations beyond Gaussian operations with a feasible input set of coherent states and standard homodyne measurements.Comment: 12 pages, 2 figures. Accepted for publication in Phys. Rev.