02547nas a2200205 4500008004100000245006500041210006400106260001400170490000900184520193000193653002702123653003102150100002002181700002202201700002302223700002202246700001702268700001902285856003702304 2023 eng d00aTime-energy uncertainty relation for noisy quantum metrology0 aTimeenergy uncertainty relation for noisy quantum metrology c12/5/20230 v4(4)3 a

Detection of weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. We consider a quantum system initialized in a pure state and whose evolution is goverened by a Hamiltonian H; a measurement can later estimate the time t for which the system has evolved. In this work, we introduce and study a fundamental trade-off which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. Specifically, we consider an idealized scenario in which Alice prepares an initial pure state of the clock, allows the clock to evolve for a time t that is not precisely known, and then transmits the clock through a noisy channel to Bob. The environment (Eve) receives any information that is lost. We prove that Bob's loss of quantum Fisher information (QFI) about t is equal to Eve's gain of QFI about a complementary energy parameter. We also prove a more general trade-off that applies when Bob and Eve wish to estimate the values of parameters associated with two non-commuting observables. We derive the necessary and sufficient conditions for the accuracy of the clock to be unaffected by the noise. These are a subset of the Knill-Laflamme error-correction conditions; states satisfying these conditions are said to form a metrological code. We provide a scheme to construct metrological codes in the stabilizer formalism. We show that there are metrological codes that cannot be written as a quantum error-correcting code with similar distance in which the Hamiltonian acts as a logical operator, potentially offering new schemes for constructing states that do not lose any sensitivity upon application of a noisy channel. We discuss applications of our results to sensing using a many-body state subject to erasure or amplitude-damping noise.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aFaist, Philippe1 aWoods, Mischa, P.1 aAlbert, Victor, V.1 aRenes, Joseph, M.1 aEisert, Jens1 aPreskill, John uhttps://arxiv.org/abs/2207.1370700958nas a2200157 4500008004100000245004700041210004600088260001500134520045900149653004300608653002700651653003100678653003100709100002300740856003700763 2022 eng d00aBosonic coding: introduction and use cases0 aBosonic coding introduction and use cases c11/10/20223 a

Bosonic or continuous-variable coding is a field concerned with robust quantum information processing and communication with electromagnetic signals or mechanical modes. I review bosonic quantum memories, characterizing them as either bosonic stabilizer or bosonic Fock-state codes. I then enumerate various applications of bosonic encodings, four of which circumvent no-go theorems due to the intrinsic infinite-dimensionality of bosonic systems.

10aFOS: Computer and information sciences10aFOS: Physical sciences10aInformation Theory (cs.IT)10aQuantum Physics (quant-ph)1 aAlbert, Victor, V. uhttps://arxiv.org/abs/2211.0571401776nas a2200181 4500008004100000245004200041210004100083260001400124520125200138653002701390653003101417100002301448700002301471700002001494700002201514700002101536856003701557 2022 eng d00aContinuous-Variable Shadow Tomography0 aContinuousVariable Shadow Tomography c11/9/20223 a

Shadow tomography is a framework for constructing succinct descriptions of quantum states, called classical shadows, with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable tomography in the classical-shadow framework, obtaining rigorous bounds on the sample complexity for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon number resolving (PNR), and photon-parity protocols. To reach a desired precision on the classical shadow of an N-photon density matrix with a high probability, we show that homodyne detection requires an order O(N5) measurements in the worst case, whereas PNR and photon-parity detection require O(N4) measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental homodyne tomography significantly outperforms our bounds, exhibiting a more typical scaling of the number of measurements that is close to linear in N. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aGandhari, Srilekha1 aAlbert, Victor, V.1 aGerrits, Thomas1 aTaylor, Jacob, M.1 aGullans, Michael uhttps://arxiv.org/abs/2211.0514901846nas a2200181 4500008004100000245009600041210006900137260001400206520121100220653003801431653004301469653002701512653003101539100001501570700001901585700002301604856003701627 2022 eng d00aGroup coset monogamy games and an application to device-independent continuous-variable QKD0 aGroup coset monogamy games and an application to deviceindepende c12/7/20223 a

We develop an extension of a recently introduced subspace coset state monogamy-of-entanglement game [Coladangelo, Liu, Liu, and Zhandry; Crypto'21] to general group coset states, which are uniform superpositions over elements of a subgroup to which has been applied a group-theoretic generalization of the quantum one-time pad. We give a general bound on the winning probability of a monogamy game constructed from subgroup coset states that applies to a wide range of finite and infinite groups. To study the infinite-group case, we use and further develop a measure-theoretic formalism that allows us to express continuous-variable measurements as operator-valued generalizations of probability measures.
We apply the monogamy game bound to various physically relevant groups, yielding realizations of the game in continuous-variable modes as well as in rotational states of a polyatomic molecule. We obtain explicit strong bounds in the case of specific group-space and subgroup combinations. As an application, we provide the first proof of one sided-device independent security of a squeezed-state continuous-variable quantum key distribution protocol against general coherent attacks.

10aCryptography and Security (cs.CR)10aFOS: Computer and information sciences10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aCulf, Eric1 aVidick, Thomas1 aAlbert, Victor, V. uhttps://arxiv.org/abs/2212.03935