Certifying quantumness: Benchmarks for the optimal processing of generalized coherent and squeezed states

Yang, Yuxiang; Chiribella, Giulio; Adesso, Gerardo

doi:10.1103/physreva.90.042319

Cited by 28 publications

(39 citation statements)

References 86 publications

(210 reference statements)

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“…Such a feature is not an accident: we show that, unless the states commute, every asymptotically faithful protocol must use a non-zero amount of quantum memory. This result extends an observation made in [20] from certain families of pure states to generic families of states.…”

Section: Introductionsupporting

confidence: 88%

Compression for quantum population coding

Yang

Bai

Chiribella

et al. 2017

2017 IEEE International Symposium on Information Theory (ISIT)

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Abstract-We study the compression of n quantum systems, each prepared in the same state belonging to a given parametric family of quantum states. For a family of states with f independent parameters, we devise an asymptotically faithful protocol that requires a hybrid memory of size (f /2) log n, including both quantum and classical bits. Our construction uses a quantum version of local asymptotic normality and, as an intermediate step, solves the problem of compressing displaced thermal states of n identically prepared modes. In both cases, we show that (f /2) log n is the minimum amount of memory needed to achieve asymptotic faithfulness. In addition, we analyze how much of the memory needs to be quantum. We find that the ratio between quantum and classical bits can be made arbitrarily small, but cannot reach zero: unless all the quantum states in the family commute, no protocol using only classical bits can be faithful, even if it uses an arbitrarily large number of classical bits.

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Section: Introductionsupporting

confidence: 88%

Compression for quantum population coding

Yang

Bai

Chiribella

et al. 2017

2017 IEEE International Symposium on Information Theory (ISIT)

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“…Our result generalizes several previous studies partially addressing similar questions. For example in [7,[25][26][27][28] the fidelity was maximized over classical strategies (i.e., with zero shared entanglement) identifying the classical benchmark for different input sets. For a fixed entanglement, the optimal average fidelity for teleporting coherent states was studied in [17,29], albeit assuming an ideal flat distribution with unbounded variance.…”

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confidence: 99%

Optimal Continuous Variable Quantum Teleportation with Limited Resources

et al. 2017

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Given a certain amount of entanglement available as a resource, what is the most efficient way to accomplish a quantum task? We address this question in the relevant case of continuous variable quantum teleportation protocols implemented using two-mode Gaussian states with a limited degree of entanglement and energy. We first characterize the class of single-mode phase-insensitive Gaussian channels that can be simulated via a Braunstein-Kimble protocol with non-unit gain and minimum shared entanglement, showing that infinite energy is not necessary apart from the special cases of the quantum limited attenuator and amplifier. We also find that, apart from the identity, all phase-insensitive Gaussian channels can be simulated through a two-mode squeezed state with finite energy, albeit with a larger entanglement. We then consider the problem of teleporting single-mode coherent states with Gaussian-distributed displacement in phase space. Performing a geometrical optimization over phase-insensitive Gaussian channels, we determine the maximum average teleportation fidelity achievable with any finite entanglement and for any realistically finite variance of the input distribution.Determining the ultimate performance of quantum technologies in the presence of limited resources is essential to gauge their usefulness in the real world. Quantum teleportation [1, 2] enables the "disembodied transfer" of an unknown quantum state from a sender to a remote receiver, usually named Alice and Bob, respectively. To accomplish this, they need to share a quantum resource, i.e., an entangled state, and to classically communicate. Ideally, if the resource is maximally entangled, Bob can retrieve an exact copy of the input state. Unfortunately this is unrealistic, especially for continuous variable systems [3][4][5], where maximal entanglement can be obtained only in the unphysical limit of infinite energy [2,6]. It is thus important to identify the most efficient teleportation schemes, which make optimal use of limited quantum resources to achieve the largest fidelity between input and output, averaged over a specified set of input states [7]. For discrete variable systems, with uniformly sampled pure input states, a relation between such optimal fidelity and the entanglement of the resource was found in [8]. This Letter solves such a problem in a prominent continuous variable scenario.A practical protocol for continuous variable teleportation, which employs a two-mode (finitely) squeezed state as a quantum resource at the price of realizing an imperfect teleportation, was proposed by Braunstein and Kimble (BK) [9] and implemented in several experiments [10][11][12]. A characteristic feature of the BK protocol is that the input and output states are connected by a Gaussian additive noise channel [13]. Moreover, by simply introducing a non-unit classical gain in the BK protocol [10, 14-16], more general effective Gaussian channels can be "simulated" by teleportation, including quantum attenuators and amplifiers. A natural question em...

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“…continuous degrees of freedom has a quite different nature [87]. As some experimental tests of quantum memories involve continuous degrees of freedom [88,89], we leave as an open question the generalization of our results to infinite dimensional systems. Preexisting randomness, represented in our formulas by the index µ, plays an important role in the definition of entanglement-breaking channels (1) and free transformations (2), as it is the basic ingredient that provides convexity to sets of objects.…”

Section: Resultsmentioning

confidence: 89%

Resource Theory of Quantum Memories and Their Faithful Verification with Minimal Assumptions

2018

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We provide a complete set of game-theoretic conditions equivalent to the existence of a transformation from one quantum channel into another one, by means of classically correlated pre/post processing maps only. Such conditions naturally induce tests to certify that a quantum memory is capable of storing quantum information, as opposed to memories that can be simulated by measurement and state preparation (corresponding to entanglement-breaking channels). These results are formulated as a resource theory of genuine quantum memories (correlated in time), mirroring the resource theory of entanglement in quantum states (correlated spatially). As the set of conditions is complete, the corresponding tests are faithful, in the sense that any non entanglement-breaking channel can be certified. Moreover, they only require the assumption of trusted inputs, known to be unavoidable for quantum channel verification. As such, the tests we propose are intrinsically different from the usual process tomography, for which the probes of both the input and the output of the channel must be trusted. An explicit construction is provided and shown to be experimentally realizable, even in the presence of arbitrarily strong losses in the memory or detectors.Consider a vendor selling quantum devices purportedly able of storing quantum information for a period of time. However, during their operation, the devices always break the entanglement between the stored subsystem and any other subsystem. Such devices are arguably useless as quantum memories; for example, they would not be able to establish entangled links in a quantum repeater scheme [1,2]. In the terminology of quantum channels [3][4][5], those devices correspond to entanglementbreaking (EB) channels [6,7], which are exactly equivalent to the measure-and-prepare channels depicted in Fig. 1. Measure-and-prepare channels are implemented by measuring the input state, storing the classical information corresponding to the measurement outcome for the required duration, and then using that information to prepare a quantum state. Even though strictly speaking, such channels are quantum channels (since they act upon an input quantum system), they actually transmit only classical information from the input to the output. Thus, in constructing a quantum memory, one aims to produce a device that could retain some correlations between the stored system and remote systems.Due to its relevance in quantum information science, the benchmarking of quantum memories has been extensively considered in the literature [8][9][10][11][12]. An obvious way to verify whether a channel is EB or not is by performing process tomography [13][14][15], that is, by feeding through the channel a tomographically complete set of states and performing a tomographically complete measurement at the output. By collecting sufficient statistics, it is possible to reconstruct the process matrix corresponding to the channel up to any desired level of accuracy, and check whether the channel is EB or not. This scheme, however...

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Certifying quantumness: Benchmarks for the optimal processing of generalized coherent and squeezed states

Cited by 28 publications

References 86 publications

Compression for quantum population coding

Compression for quantum population coding

Optimal Continuous Variable Quantum Teleportation with Limited Resources

Resource Theory of Quantum Memories and Their Faithful Verification with Minimal Assumptions

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