Fidelity Criterion for Quantum-Domain Transmission and Storage of Coherent States Beyond the Unit-Gain Constraint

Abstract

We generalize the experimental success criterion for quantum teleportation/memory in continuous-variable quantum systems to be suitable for non-unit-gain condition by considering attenuation/amplification of the coherent-state amplitude. The new criterion can be used for a non-ideal quantum memory and long distance quantum communication as well as quantum devices with amplification process. It is also shown that the framework to measure the average fidelity is capable of detecting all Gaussian channels in quantum domain.In quantum information science [1], the manipulation of a quantum system is considered to be a channel that transforms a set of quantum states to another set of quantum states. A fundamental distinction is posed on the channel whether it can be simulated by a measure-and-prepare (M&P) scheme or not. The M&P scheme implies that the output of the channel is produced merely based on the classical data processing from the measurement outcomes and that the channel action breaks quantum entanglement shared between the input of the channel and other systems [2]. Therefore, a natural benchmark for the quantum-domain (QD) operation of a given experimental quantum manipulation is that the channel is outperforming any M&P scheme. The M&P scheme is an intercept-resend attack in the context of the quantum key distribution (QKD), and no secret key can be generated if the input-output relation is explained by an M&P scheme. Hence confirming the QD operation is an important prerequisite for any QKD [3,4]. Hammerer et al. [5] have established the criterion for the QD operation of continuous-variable (CV) channels by proving a limit of the average fidelity achievable by the M&P schemes, Fc, assuming an input set of coherent states: Surpassing Fc ensures the QD operation for transmission and storage of coherent states. This criterion gave a proof for the long-standing conjecture of CV quantum teleportation about Fc [6,7] and provided a firm foundation for the central claims of experimental CV quantum teleportation [7,8,9] and quantum memory [10]. However, the application of this criterion is limited to the unit-gain (UG) channels where the coherent-state amplitudes of the input state and the output state are expected to be the same [9,11].Quantum memory for light (QM) is a challenging protocol [12,13], which requires UG operation and involves not only storage of the states but also transfer of the states between different physical media, such as an optical system and an atomic ensemble. In any implementation [10,14,15,16], it is likely that the effect of linear loss or damping of coherent-state amplitude becomes more significant as the storage period becomes longer. Therefore, some mechanism of gain adjustments seems to be necessary for the complete demonstration of QM. With gain control of the teleportation-based state transfer [12], an above-Fc operation of QM has been reported [10]. Another possible solution for the gain control is to employ an amplifier [17], where it is shown that the quantumlimit phase-insens...

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

“…Quite surprisingly, the value of the probabilistic benchmark coincides with the value of the deterministic benchmark obtained in Ref. [17], implying that probabilistic MP protocols offer no advantage over deterministic ones in the case of coherent states. All these findings can be obtained from the general result of Theorem 1.…”

“…For N = M = 1, the above value coincides with the teleportation benchmark conjectured in [6] and proven in [9], which converges to 1 2 for uniform prior distribution (λ → 0). For general N and M, it reproduces the various bounds given in [16][17][18].…”

“…Later, benchmarks for deterministic amplification and attenuation were put forward by Namiki et al [17]. More recently, Chiribella and Xie derived the quantum benchmark for probabilistic amplification of coherent states [18].…”

“…Benchmarks applicable to other protocols have been developed as well. Benchmarks for nonunit-gain protocols, which include amplification, attenuation, and N → M quantum cloning of qubits, qudits, and coherent states, have been studied in detail [8,[15][16][17][18]; they reduce to the corresponding results for teleportation in particular limits (e.g., in the case of cloning for N = M = 1). Finally, an alternative approach to quantum benchmarks, testing the ability of a quantum device to transmit entanglement, has also been put forward [19][20][21].…”

Einstein–Podolsky–Rosen-Like Correlation on a Coherent-State Basis and Inseparability of Two-Mode Gaussian States

“…The condition of Eq. (3) was formulated for the quantum benchmark problem [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], however, its utility and significance for the separability problem have little been discussed.…”