arXiv subjects

Eric Chitambar

Publications and source records attributed to Eric Chitambar.

At least 73 records · Page 4Linked to original sources

arXiv2020

Bounds on Instantaneous Nonlocal Quantum Computation

Instantaneous nonlocal quantum computation refers to a process in which spacelike separated parties simulate a nonlocal quantum operation on their joint systems through the consumption of pre-shared entanglement. To prevent a violation of causality, this simulation succeeds up to local errors that can only be corrected after the parties communicate classically with one another. However, this communication is non-interactive, and it involves just the broadcasting of local measurement outcomes. We refer to this operational paradigm as local operations and broadcast communication (LOBC) to distinguish it from the standard local operations and (interactive) classical communication (LOCC). In this paper, we show that an arbitrary two-qubit gate can be implemented by LOBC with $ε$-error using $O(\log(1/ε))$ entangled bits (ebits). This offers an exponential improvement over the best known two-qubit protocols, whose ebit costs behave as $O(1/ε)$. We also consider the family of binary controlled gates on dimensions $d_A\otimes d_B$. We find that any hermitian gate of this form can be implemented by LOBC using a single shared ebit. In sharp contrast, a lower bound of $\log d_B$ ebits is shown in the case of generic (i.e. non-hermitian) gates from this family, even when $d_A=2$. This demonstrates an unbounded gap between the entanglement costs of LOCC and LOBC gate implementation. Whereas previous lower bounds on the entanglement cost for instantaneous nonlocal computation restrict the minimum dimension of the needed entanglement, we bound its entanglement entropy. To our knowledge this is the first such lower bound of its kind.

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arXiv2020

A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability

Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely non-classical phenomenon provides a necessary ingredient in many quantum information tasks such violating a Bell Inequality or nonlocally steering part of an entangled state. In this paper, we characterize incompatibility in terms of programmable measurement devices and the general notion of quantum programmability. This refers to the temporal freedom a user has in issuing programs to a quantum device. For devices with a classical control and classical output, measurement incompatibility emerges as the essential quantum resource embodied in their functioning. Based on the processing of programmable measurement devices, we construct a quantum resource theory of incompatibility. A complete set of convertibility conditions for programmable devices is derived based on quantum state discrimination with post-measurement information.

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arXiv2019

Channel Activation of CHSH Nonlocality

Quantum channels that break CHSH nonlocality on all input states are known as CHSH-breaking channels. In quantum networks, such channels are useless for distributing correlations that can violate the CHSH Inequality. Motivated by previous work on activation of nonlocality in quantum states, here we demonstrate an analogous activation of CHSH-breaking channels. That is, we show that certain pairs of CHSH-breaking channels are no longer CHSH-breaking when used in combination. We find that this type of activation can emerge in both uni-directional and bi-directional communication scenarios.

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arXiv2019

Dynamical Resource Theory of Quantum Coherence

Decoherence is all around us. Every quantum system that interacts with the environment is doomed to decohere. The preservation of quantum coherence is one of the major challenges faced in quantum technologies, but its use as a resource is very promising and can lead to various operational advantages, for example in quantum algorithms. Hence, much work has been devoted in recent years to quantify the coherence present in a system. In the present paper, we formulate the quantum resource theory of dynamical coherence. The underlying physical principle we follow is that the free dynamical objects are those that cannot preserve or distribute coherence. This leads us to identify classical channels as the free elements in this theory. Consequently, even the quantum identity channel is not free as all physical systems undergo decoherence and hence, the preservation of coherence should be considered a resource. In our work, we introduce four different types of free superchannels (analogous to MIO, DIO, IO, and SIO) and discuss in detail two of them, namely, dephasing-covariant incoherent superchannels (DISC), maximally incoherent superchannels (MISC). The latter consists of all superchannels that do not generate non-classical channels from classical ones. We quantify dynamical coherence using channel-divergence-based monotones for MISC and DISC. We show that some of these monotones have operational interpretations as the exact, the approximate, and the liberal coherence cost of a quantum channel. Moreover, we prove that the liberal asymptotic cost of a channel is equal to a new type of regularized relative entropy. Finally, we show that the conversion distance between two channels under MISC and DISC can be computed using a semi-definite program (SDP).

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arXiv2019

Entanglement manipulation and distillability beyond LOCC

When a quantum system is distributed to spatially separated parties, it is natural to consider how the system evolves when the parties perform local quantum operations with classical communication (LOCC). However, the structure of LOCC channels is exceedingly complex leaving many important physical problems unsolved. In this paper we consider generalized resource theories of entanglement based on different relaxations to the class of LOCC. The behavior of various entanglement measures is studied under non-entangling channels, as well as the newly introduced classes of dually non-entangling and PPT-preserving channels. In an effort to better understand the nature of LOCC bound entanglement, we study the problem of entanglement distillation in these generalized resource theories. We first show that unlike LOCC, general non-entangling maps can be superactivated, in the sense that two copies of the same non-entangling map can nevertheless be entangling. On the single-copy level, we demonstrate that every NPT entangled state can be converted into an LOCC-distillable state using channels that are both dually non-entangling and having a PPT Choi representation and that every state can be converted into an LOCC-distillable state using operations belonging to any family of polytopes that approximate LOCC. We then turn to the stochastic convertibility of multipartite pure states and show that any two states can be interconverted by any polytope approximation to the set of separable channels. Finally, as an analog to $k$-positive maps, we introduce and analyze the set of $k$-non-entangling channels.

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arXiv2019

Quantum Resource Theories

Quantum resource theories (QRTs) offer a highly versatile and powerful framework for studying different phenomena in quantum physics. From quantum entanglement to quantum computation, resource theories can be used to quantify a desirable quantum effect, develop new protocols for its detection, and identify processes that optimize its use for a given application. Particularly, QRTs revolutionize the way we think about familiar properties of physical systems like entanglement, elevating them from just being interesting from a fundamental point of view to being useful in performing practical tasks. The basic methodology of a general QRT involves partitioning all quantum states into two groups, one consisting of free states and the other consisting of resource states. Accompanying the set of free states is a collection of free quantum operations arising from natural restrictions on physical systems, and that consists of all the physical processes allowed by the resource theory and which acts invariantly on the set of free states. The QRT then studies what information processing tasks become possible using the restricted operations. Despite the large degree of freedom in how one defines the free states and free operations, unexpected similarities emerge among different QRTs in terms of resource measures and resource convertibility. As a result, objects that appear quite distinct on the surface, such as entanglement and quantum reference frames, appear to have great similarity on a deeper structural level. In this article we review the general framework of a quantum resource theory, focusing on common structural features, operational tasks, and resource measures. To illustrate these concepts, an overview is provided on some of the more commonly studied QRTs in the literature.

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arXiv2019

One-Shot Coherence Distillation: Towards Completing the Picture

The resource framework of quantum coherence was introduced by Baumgratz, Cramer and Plenio [PRL 113, 140401 (2014)] and further developed by Winter and Yang [PRL 116, 120404 (2016)]. We consider the one-shot problem of distilling pure coherence from a single instance of a given resource state. Specifically, we determine the distillable coherence with a given fidelity under incoherent operations (IO) through a generalisation of the Winter-Yang protocol. This is compared to the distillable coherence under maximal incoherent operations (MIO) and dephasing-covariant incoherent operations (DIO), which can be cast as a semidefinite programme, that has been presented previously by Regula et al. [PRL 121, 010401 (2018)]. Our results are given in terms of a smoothed min-relative entropy distance from the incoherent set of states, and a variant of the hypothesis-testing relative entropy distance, respectively. The one-shot distillable coherence is also related to one-shot randomness extraction. Moreover, from the one-shot formulas under IO, MIO, DIO, we can recover the optimal distillable rate in the many-copy asymptotics, yielding the relative entropy of coherence. These results can be compared with previous work by some of the present authors [Zhao et al., PRL 120, 070403 (2018)] on one-shot coherence formation under IO, MIO, DIO and also SIO. This shows that the amount of distillable coherence is essentially the same for IO, DIO, and MIO, despite the fact that the three classes of operations are very different. We also relate the distillable coherence under strictly incoherent operations (SIO) to a constrained hypothesis testing problem and explicitly show the existence of bound coherence under SIO in the asymptotic regime.

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arXiv2018

One-Shot Coherence Dilution

Manipulation and quantification of quantum resources are fundamental problems in quantum physics. In the asymptotic limit, coherence distillation and dilution have been proposed by manipulating infinite identical copies of states. In the non-asymptotic setting, finite data-size effects emerge, and the practically relevant problem of coherence manipulation using finite resources has been left open. This letter establishes the one-shot theory of coherence dilution, which involves converting maximally coherent states into an arbitrary quantum state using maximally incoherent operations, dephasing-covariant incoherent operations, incoherent operations, or strictly incoherent operations. We introduce several coherence monotones with concrete operational interpretations that estimate the one-shot coherence cost --- the minimum amount of maximally coherent states needed for faithful coherence dilution. Furthermore, we derive the asymptotic coherence dilution results with maximally incoherent operations, incoherent operations, and strictly incoherent operations as special cases. Our result can be applied in the analyses of quantum information processing tasks that exploit coherence as resources, such as quantum key distribution and random number generation.

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arXiv2018

The Zero-error Entanglement Cost is Highly Non-Additive

The Schmidt number is an entanglement measure whose logarithm quantifies the zero-error entanglement cost of generating a given quantum state using local operations and classical communication (LOCC). %However, the Schmidt number is a notoriously difficult quantity to compute, and its relationship to other entanglement measures is largely unknown. In this paper we show that the Schmidt number is highly non-multiplicative in the sense that for any integer $n$, there exists states whose Schmidt number remains constant when taking $n$ copies of the given state. These states also provide a rare instance in which the regularized zero-error entanglement cost can be computed exactly. We then explore the question of increasing the Schmidt number by quantum operations. We describe a class of bipartite quantum operations that preserve the Schmidt number for pure state transformations, and yet they can increase the Schmidt number by an arbitrarily large amount when generating mixed states. Our results are obtained by making connections to the resource theory of quantum coherence and generalizing the class of dephasing-covariant incoherent operations (DIO) to the bipartite setting.

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arXiv2018

Common Resource State for Preparing Multipartite Quantum Systems via Local Operations and Classical Communication

Given a set of multipartite entangled states, can we find a common state to prepare them by local operations and classical communication? Such a state, if exists, will be a common resource for the given set of states. We completely solve this problem for bipartite pure states case by explicitly constructing a unique optimal common resource state for any given set of states. In the multipartite setting, the general problem becomes quite complicated, and we focus on finding nontrivial common resources for the whole multipartite state space of given dimensions. We show that GHZ_3 is a nontrivial common resource for three-qubit systems.

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arXiv2018

One-shot assisted concentration of coherence

We find one-shot bounds for concentration of maximally coherent states in the so called assisted scenario. In this setting, Bob is restricted to performing incoherent operations on his quantum system, however he is assisted by Alice, who holds a purification of Bob's state and can send classical data to him. We further show that in the asymptotic limit our one-shot bounds recover the previously computed rate of asymptotic assisted concentration.

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arXiv2018

More Nonlocality with Less Entanglement in CHSH Experiments using Inefficient Detectors

It is well-known that in certain scenarios weakly entangled states can generate stronger nonlocal effects than their maximally entangled counterparts. In this paper, we consider violations of the CHSH Inequality when one party has inefficient detectors, a scenario known as an asymmetric Bell experiment. %We show that violations can occur if and only if the detection efficiency is above $50\%$. For any fixed detection efficiency, we derive a simple upper bound on the entanglement needed to violate the inequality by more than some specified amount $κ\geq 0$. When $κ=0$, the amount of entanglement in all states violating the inequality goes to zero as the detection efficiency approaches $50\%$ from above. %This provides another scenario in which weakly entangled states are advantageous for violating the CHSH Inequality in the presence of detection inefficiency. We finally consider the scenario in which detection inefficiency arises for only one choice of local measurement. In this case, it is shown that the CHSH Inequality can always be violated for any nonzero detection efficiency and any choice of non-commuting measurements.

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arXiv2017

Dephasing-Covariant Operations Enable Asymptotic Reversibility of Quantum Resources

We study the power of dephasing-covariant operations in the resource theories of coherence and entanglement. These are quantum operations whose actions commute with a projective measurement. In the resource theory of coherence, we find that any two states are asymptotically interconvertible under dephasing-covariant operations. This provides a rare example of a resource theory in which asymptotic reversibility can be attained without needing the maximal set of resource non-generating operations. When extended to the resource theory of entanglement, the resultant operations share similarities with LOCC, such as prohibiting the increase of all Rényi $α$-entropies of entanglement under pure state transformations. However, we show these operations are still strong enough to enable asymptotic reversibility between any two maximally correlated mixed states, even in the multipartite setting.

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arXiv2016

Round Complexity in the Local Transformations of Quantum and Classical States

A natural operational paradigm for distributed quantum and classical information processing involves local operations coordinated by multiple rounds of public communication. In this paper we consider the minimum number of communication rounds needed to perform the locality-constrained task of entanglement transformation and the analogous classical task of secrecy manipulation. Specifically we address whether bipartite mixed entanglement can always be converted into pure entanglement or whether unsecure classical correlations can always be transformed into secret shared randomness using local operations and a bounded number of communication exchanges. Our main contribution in this paper is an explicit construction of quantum and classical state transformations which, for any given $r$, can be achieved using $r$ rounds of classical communication exchanges but no fewer. Our results reveal that highly complex communication protocols are indeed necessary to fully harness the information-theoretic resources contained in general quantum and classical states. The major technical contribution of this manuscript lies in proving lower bounds for the required number of communication exchanges using the notion of common information and various lemmas built upon it. We propose a classical analog to the Schmidt rank of a bipartite quantum state which we call the secrecy rank, and we show that it is a monotone under stochastic local classical operations.

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arXiv2016

Loss-tolerant quantum secure positioning with weak laser sources

Quantum position verification (QPV) is the art of verifying the geographical location of an untrusted party. Recently, it has been shown that the widely studied Bennett & Brassard 1984 (BB84) QPV protocol is insecure after the 3 dB loss point assuming local operations and classical communication (LOCC) adversaries. Here, we propose a time-reversed entanglement swapping QPV protocol (based on measurement-device-independent quantum cryptography) that is highly robust against quantum channel loss. First, assuming ideal qubit sources, we show that the protocol is secure against LOCC adversaries for any quantum channel loss, thereby overcoming the 3 dB loss limit. Then, we analyze the security of the protocol in a more practical setting involving weak laser sources and linear optics. In this setting, we find that the security only degrades by an additive constant and the protocol is able to verify positions up to 47 dB channel loss.

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arXiv2016

Relating the Resource Theories of Entanglement and Quantum Coherence

Quantum coherence and quantum entanglement represent two fundamental features of non-classical systems that can each be characterized within an operational resource theory. In this paper, we unify the resource theories of entanglement and coherence by studying their combined behavior in the operational setting of local incoherent operations and classical communication (LIOCC). Specifically we analyze the coherence and entanglement trade-offs in the tasks of state formation and resource distillation. For pure states we identify the minimum coherence-entanglement resources needed to generate a given state, and we introduce a new LIOCC monotone that completely characterizes a state's optimal rate of bipartite coherence distillation. This result allows us to precisely quantify the difference in operational powers between global incoherent operations, LIOCC, and local incoherent operations \textit{without} classical communication. Finally, a bipartite mixed state is shown to have distillable entanglement if and only if entanglement can be distilled by LIOCC, and we strengthen the well-known Horodecki criterion for distillability.

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arXiv2016

Are Incoherent Operations Physically Consistent? -- A Critical Examination of Incoherent Operations

Considerable work has recently been directed toward developing resource theories of quantum coherence. In most approaches, a state is said to possess quantum coherence if it is not diagonal in some specified basis. In this letter we establish a criterion of physical consistency for any resource theory in terms of physical implementation of the free operations, and we show that all currently proposed basis-dependent theories of coherence fail to satisfy this criterion. We further characterize the physically consistent resource theory of coherence and find its operational power to be quite limited. After relaxing the condition of physical consistency, we introduce the class of dephasing-covariant incoherent operations, present a number of new coherent monotones based on relative Rényi entropies, and study incoherent state transformations under different operational classes. In particular, we derive necessary and sufficient conditions for qubit state transformations and show these conditions hold for all classes of incoherent operations.

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arXiv2015

Quantum Versus Classical Advantages in Secret Key Distillation (and Their Links to Quantum Entanglement)

We consider the extraction of shared secret key from correlations that are generated by either a classical or quantum source. In the classical setting, two honest parties (Alice and Bob) use public discussion and local randomness to distill secret key from some distribution $p_{XYZ}$ that is shared with an unwanted eavesdropper (Eve). In the quantum settings, the correlations $p_{XYZ}$ are delivered to the parties as either an \textit{incoherent} mixture of orthogonal quantum states or as \textit{coherent} superposition of such states; in both cases, Alice and Bob use public discussion and local quantum operations to distill secret key. While the power of quantum mechanics increases Alice and Bob's ability to generate shared randomness, it also equips Eve with a greater arsenal of eavesdropping attacks. Therefore, it is not obvious who gains the greatest advantage for distilling secret key when replacing a classical source with a quantum one. In this paper we first demonstrate that the classical key rate is equivalent to the quantum key rate when the correlations are generated incoherently in the quantum setting. For coherent sources, we next show that the rates are incomparable, and in fact, their difference can be arbitrarily large in either direction. However, we identify a large class of non-trivial distributions $p_{XYZ}$ that possess the following properties: (i) Eve's advantage is always greater in the quantum source than in its classical counterpart, and (ii) for the quantum entanglement shared between Alice and Bob in the coherent source, the so-called entanglement cost/squashed entanglement/relative entropy of entanglement can all be computed. With property (ii), we thus present a rare instance in which the various entropic entanglement measures of a quantum state can be explicitly calculated.

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