Visually quantifying single-qubit quantum memory
Abstract: To store quantum information, quantum memory plays a central intermediate ingredient in a network. The minimal criterion for a reliable quantum memory is the maintenance of the entangled state, which can be described by the non-entanglement-breaking (non-EB) channel. In this work, we show that all single-qubit quantum memory can be quantified without trusting input state generation. In other words, we provide a semi-device-independent approach to quantify all single-qubit quantum memory. More specifically, we apply the concept of the two-qubit quantum steering ellipsoids to a single-qubit quantum channel and define the channel ellipsoids. An ellipsoid can be constructed by visualizing finite output states within the Bloch sphere. Since the Choi-Jamio{\l}kowski state of a channel can all be reconstructed from geometric data of the channel ellipsoid, a reliable quantum memory can be detected. Finally, we visually quantify the single-qubit quantum memory by observing the volume of the channel ellipsoid.
- A. I. Lvovsky, B. C. Sanders, and W. Tittel, Optical quantum memory, Nature Photonics 3, 706 (2009).
- A. S. Holevo, Entanglement-breaking channels in infinite dimensions, Problems of Information Transmission 44, 171 (2008).
- M. Horodecki, P. W. Shor, and M. B. Ruskai, Entanglement breaking channels, Rev. Math. Phys. 15, 629 (2003).
- M. B. Ruskai, Qubit entanglement breaking channels, Rev. Math. Phys. 15, 643 (2003).
- A. K. Ekert, Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett. 67, 661 (1991).
- M. F. Pusey, Verifying the quantumness of a channel with an untrusted device, J. Opt. Soc. Am. B 32, A56 (2015).
- C. Budroni, G. Fagundes, and M. Kleinmann, Memory cost of temporal correlations, New Journal of Physics 21, 093018 (2019).
- L. B. Vieira and C. Budroni, Temporal correlations in the simplest measurement sequences, Quantum 6, 623 (2022).
- D. Rosset, F. Buscemi, and Y.-C. Liang, Resource theory of quantum memories and their faithful verification with minimal assumptions, Phys. Rev. X 8, 021033 (2018).
- P. Abiuso, Verification of Continuous-Variable Quantum Memories, arXiv e-prints , arXiv:2305.07513 (2023), arXiv:2305.07513 [quant-ph] .
- F. Buscemi, All entangled quantum states are nonlocal, Phys. Rev. Lett. 108, 200401 (2012).
- D. Rosset, D. Schmid, and F. Buscemi, Type-independent characterization of spacelike separated resources, Phys. Rev. Lett. 125, 210402 (2020).
- D. Schmid, D. Rosset, and F. Buscemi, The type-independent resource theory of local operations and shared randomness, Quantum 4, 262 (2020).
- Y.-C. Liang, T. Vértesi, and N. Brunner, Semi-device-independent bounds on entanglement, Phys. Rev. A 83, 022108 (2011).
- N. Miklin and M. Oszmaniec, A universal scheme for robust self-testing in the prepare-and-measure scenario, Quantum 5, 424 (2021).
- D. Cavalcanti and P. Skrzypczyk, Quantum steering: a review with focus on semidefinite programming, Reports on Progress in Physics 80, 024001 (2016).
- R. McCloskey, A. Ferraro, and M. Paternostro, Einstein-podolsky-rosen steering and quantum steering ellipsoids: Optimal two-qubit states and projective measurements, Phys. Rev. A 95, 012320 (2017).
- H.-Y. Ku, C.-Y. Hsieh, and C. Budroni, Measurement incompatibility cannot be stochastically distilled, arXiv e-prints , arXiv:2308.02252 (2023), arXiv:2308.02252 [quant-ph] .
- P. Skrzypczyk and D. Cavalcanti, Maximal randomness generation from steering inequality violations using qudits, Phys. Rev. Lett. 120, 260401 (2018).
- C.-Y. Hsieh, H.-Y. Ku, and C. Budroni, Characterisation and fundamental limitations of irreversible stochastic steering distillation, arXiv e-prints , arXiv:2309.06191 (2023), arXiv:2309.06191 [quant-ph] .
- M.-D. Choi, Completely positive linear maps on complex matrices, Linear Algebra and its Applications 10, 285 (1975).
- A. Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Reports on Mathematical Physics 3, 275 (1972).
- G. Chiribella, G. M. D’Ariano, and P. Perinotti, Theoretical framework for quantum networks, Phys. Rev. A 80, 022339 (2009).
- S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004).
- A. Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77, 1413 (1996).
- M. Horodecki, P. Horodecki, and R. Horodecki, Separability of mixed states: necessary and sufficient conditions, Physics Letters A 223, 1 (1996).
- O. Gühne and G. Tóth, Entanglement detection, Phys. Rep. 474, 1 (2009).
- W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998).
- F. Verstraete and H. Verschelde, Optimal teleportation with a mixed state of two qubits, Phys. Rev. Lett. 90, 097901 (2003).
- M. Girard, M. Plávala, and J. Sikora, Jordan products of quantum channels and their compatibility, Nature Communications 12, 2129 (2021).
- F. B. Maciejewski, Z. Zimborás, and M. Oszmaniec, Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography, Quantum 4, 257 (2020).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.