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Tal Mor

Publications and source records attributed to Tal Mor.

At least 37 records · Page 2Linked to original sources
arXiv2020

Quantum Candies and Quantum Cryptography

The field of quantum information is becoming more known to the general public. However, effectively demonstrating the concepts underneath quantum science and technology to the general public can be a challenging job. We investigate, extend, and much expand here "quantum candies" (invented by Jacobs), a pedagogical model for intuitively describing some basic concepts in quantum information, including quantum bits, complementarity, the no-cloning principle, and entanglement. Following Jacob's quantum candies description of the well known quantum key distribution protocol BB84, we explicitly demonstrate various additional quantum cryptography protocols using quantum candies in an approachable manner. The model we investigate can be a valuable tool for science and engineering educators who would like to help the general public to gain more insights about quantum science and technology: most parts of this paper, including many protocols for quantum cryptography, are expected to be easily understandable by a layperson without any previous knowledge of mathematics, physics, or cryptography.

physics.ed-ph↗
arXiv2020

Topological order on the Bloch sphere

A Bloch sphere is the geometrical representation of an arbitrary two-dimensional Hilbert space. Possible classes of entanglement and separability for the pure and mixed states on the Bloch sphere were suggested by [M. Boyer, R. Liss, T. Mor, PRA 95, 032308 (2017)]. Here we construct a Bloch sphere for the Hilbert space spanned by one of the ground states of Kitaev's toric code model and one of its closest product states. We prove that this sphere contains only one separable state, thus belonging to the fourth class suggested by the said paper. We furthermore study the topological order of the pure states on its surface and conclude that, according to conventional definitions, only one state (the toric code ground state) seems to present non-trivial topological order. We conjecture that most of the states on this Bloch sphere are neither ``trivial'' states (namely, they cannot be generated from a product state using a trivial circuit) nor topologically ordered. In addition, we show that the whole setting can be understood in terms of Grover rotations with gauge symmetry, akin to the quantum search algorithm.

quant-ph↗
arXiv2019

Composable security against collective attacks of a modified BB84 QKD protocol with information only in one basis

Quantum Cryptography uses the counter-intuitive properties of Quantum Mechanics for performing cryptographic tasks in a secure and reliable way. The Quantum Key Distribution (QKD) protocol BB84 has been proven secure against several important types of attacks: collective attacks and joint attacks. Here we analyze the security of a modified BB84 protocol, for which information is sent only in the z basis while testing is done in both the z and the x bases, against collective attacks. The proof follows the framework of a previous paper (Boyer, Gelles, and Mor, 2009), but it avoids a classical information-theoretical analysis and proves a fully composable security. We show that this modified BB84 protocol is as secure against collective attacks as the original BB84 protocol, and that it requires more bits for testing.

quant-ph↗
arXiv2018

Attacks against a Simplified Experimentally Feasible Semiquantum Key Distribution Protocol

A semiquantum key distribution (SQKD) protocol makes it possible for a quantum party and a classical party to generate a secret shared key. However, many existing SQKD protocols are not experimentally feasible in a secure way using current technology. An experimentally feasible SQKD protocol, "classical Alice with a controllable mirror" (the "Mirror protocol"), has recently been presented and proved completely robust, but it is more complicated than other SQKD protocols. Here we prove a simpler variant of the Mirror protocol (the "simplified Mirror protocol") to be completely non-robust by presenting two possible attacks against it. Our results show that the complexity of the Mirror protocol is at least partly necessary for achieving robustness.

quant-ph↗
arXiv2017

Experimentally feasible protocol for semiquantum key distribution

Quantum key distribution (QKD) protocols make it possible for two quantum parties to generate a secret shared key. Semiquantum key distribution (SQKD) protocols, such as "QKD with classical Bob" and "QKD with classical Alice" (that have both been proven robust), achieve this goal even if one of the parties is classical. However, existing SQKD protocols are not experimentally feasible with current technology. Here we suggest a new protocol, "Classical Alice with a controllable mirror", that can be experimentally implemented with current technology (using 4-level systems instead of qubits), and we prove it to be robust.

quant-ph↗
arXiv2017

Security Against Collective Attacks of a Modified BB84 QKD Protocol with Information only in One Basis

The Quantum Key Distribution (QKD) protocol BB84 has been proven secure against several important types of attacks: the collective attacks and the joint attacks. Here we analyze the security of a modified BB84 protocol, for which information is sent only in the z basis while testing is done in both the z and the x bases, against collective attacks. The proof follows the framework of a previous paper (Boyer, Gelles, and Mor, 2009), but it avoids the classical information-theoretical analysis that caused problems with composability. We show that this modified BB84 protocol is as secure against collective attacks as the original BB84 protocol, and that it requires more bits for testing.

quant-ph↗
arXiv2017

Heat-Bath Algorithmic Cooling with correlated qubit-environment interactions

Controlled preparation of highly pure quantum states is at the core of practical applications of quantum information science, from the state initialization of most quantum algorithms to a reliable supply of ancilla qubits that satisfy the fault-tolerance threshold for quantum error correction. Heat-bath algorithmic cooling has been shown to purify qubits by controlled redistribution of entropy and multiple contact with a bath, not only for ensemble implementations but also for technologies with strong but imperfect measurements. However, an implicit restriction about the interaction with the bath has been assumed in previous work. In this paper, we show that better purification can be achieved by removing that restriction. More concretely, we include correlations between the system and the bath, and we take advantage of these correlations to pump entropy out of the system into the bath. We introduce a tool for cooling algorithms, which we call "state-reset", obtained when the coupling to the environment is generalized from individual-qubits relaxation to correlated-qubit relaxation. We present improved cooling algorithms which lead to an increase of purity beyond all the previous work, and relate our results to the Nuclear Overhauser Effect.

quant-ph↗
arXiv2017

Geometry of entanglement in the Bloch sphere

Entanglement is an important concept in quantum information, quantum communication, and quantum computing. We provide a geometrical analysis of entanglement and separability for all the rank-2 quantum mixed states: complete analysis for the bipartite states, and partial analysis for the multipartite states. For each rank-2 mixed state, we define its unique Bloch sphere, that is spanned by the eigenstates of its density matrix. We characterize those Bloch spheres into exactly five classes of entanglement and separability, give examples for each class, and prove that those are the only classes.

quant-ph↗
arXiv2017

Extrapolated Quantum States, Void States, and a Huge Novel Class of Distillable Entangled States

A nice and interesting property of any pure tensor-product state is that each such state has distillable entangled states at an arbitrarily small distance $ε$ in its neighborhood. We say that such nearby states are $ε$-entangled, and we call the tensor product state in that case, a "boundary separable state", as there is entanglement at any distance from this "boundary". Here we find a huge class of separable states that also share that property mentioned above -- they all have $ε$-entangled states at any small distance in their neighborhood. Furthermore, the entanglement they have is proven to be distillable. We then extend this result to the discordant/classical cut and show that all classical states (correlated and uncorrelated) have discordant states at distance $ε$, and provide a constructive method for finding $ε$-discordant states.

quant-ph↗
arXiv2017

Entanglement and deterministic quantum computing with one qubit

The role of entanglement and quantum correlations in complex physical systems and quantum information processing devices has become a topic of intense study in the past two decades. In this work we present new tools for learning about entanglement and quantum correlations in dynamical systems where the quantum states are mixed and the eigenvalue spectrum is highly degenerate. We apply these results to the Deterministic quantum computing with one qubit (DQC1) computation model and show that the states generated in a DQC1 circuit have an eigenvalue structure that makes them difficult to entangle, even when they are relatively far from the completely mixed state. Our results strengthen the conjecture that it may be possible to find quantum algorithms that do not generate entanglement and yet still have an exponential advantage over their classical counterparts.

quant-ph↗
arXiv2016

Reversed Space Attacks

Many quantum key distribution (QKD) schemes are based on sending and measuring qubits -- two-dimensional quantum systems. Yet, in practical realizations and experiments, the measuring devices at the receiver's (Bob) site commonly do not measure a two-dimensional system but rather a quantum space of a larger dimension. Such an enlargement sometimes results from imperfect devices. However, in various QKD protocols such enlargement exists even in the ideal scenario when all devices are assumed to be perfect. This issue is common, for instance, in QKD schemes implemented via photons, where the parties' devices are based on Mach-Zehnder interferometers, as these inherently enlarge the quantum space in use. We show how space enlargement at Bob's site exposes the implemented protocol to new kinds of attacks, attacks that have not yet been explicitly pinpointed nor rigorously analyzed. We name these the "reversed space attacks". A key insight in formalizing our attacks, is the idea of taking all states defining Bob's (large) measured space and reversing them in time in order to identify precisely the space that an eavesdropper may attack. We employ such attacks on two variants of intereferometric-based QKD recently experimented by several groups, and show how to get full information on the qubit sent by Alice, while inducing no errors at all. The technique we develop here has subsequently been used in a closely related work (Boyer, Gelles, and Mor, Physical Review A, 2014) to demonstrate a (weaker variant of) reversed-space attack on both interferometric-based and polarization-based QKD.

quant-ph↗
arXiv2015

Algorithmic Cooling in Liquid State NMR

Algorithmic cooling is a method that employs thermalization to increase qubit purification level, namely it reduces the qubit-system's entropy. We utilized gradient ascent pulse engineering (GRAPE), an optimal control algorithm, to implement algorithmic cooling in liquid state nuclear magnetic resonance. Various cooling algorithms were applied onto the three qubits of $^{13}$C$_2$-trichloroethylene, cooling the system beyond Shannon's entropy bound in several different ways. In particular, in one experiment a carbon qubit was cooled by a factor of 4.61. This work is a step towards potentially integrating tools of NMR quantum computing into in vivo magnetic resonance spectroscopy.

quant-ph↗
arXiv2014

Experimental Heat-Bath Cooling of Spins

Algorithmic cooling (AC) is a method to purify quantum systems, such as ensembles of nuclear spins, or cold atoms in an optical lattice. When applied to spins, AC produces ensembles of highly polarized spins, which enhance the signal strength in nuclear magnetic resonance (NMR). According to this cooling approach, spin-half nuclei in a constant magnetic field are considered as bits, or more precisely, quantum bits, in a known probability distribution. Algorithmic steps on these bits are then translated into specially designed NMR pulse sequences using common NMR quantum computation tools. The $algorithmic$ cooling of spins is achieved by alternately combining reversible, entropy-preserving manipulations (borrowed from data compression algorithms) with $selective$ $reset$, the transfer of entropy from selected spins to the environment. In theory, applying algorithmic cooling to sufficiently large spin systems may produce polarizations far beyond the limits due to conservation of Shannon entropy. Here, only selective reset steps are performed, hence we prefer to call this process "heat-bath" cooling, rather than algorithmic cooling. We experimentally implement here two consecutive steps of selective reset that transfer entropy from two selected spins to the environment. We performed such cooling experiments with commercially-available labeled molecules, on standard liquid-state NMR spectrometers. Our experiments yielded polarizations that $bypass$ $Shannon's$ $entropy$-$conservation$ $bound$, so that the entire spin-system was cooled. This paper was initially submitted in 2005, first to Science and then to PNAS, and includes additional results from subsequent years (e.g. for resubmission in 2007). The Postscriptum includes more details.

quant-ph↗
arXiv2014

Prospects and Limitations of Algorithmic Cooling

Heat-bath algorithmic cooling (AC) of spins is a theoretically powerful effective cooling approach, that (ideally) cools spins with low polarization exponentially better than cooling by reversible entropy manipulations alone. Here, we investigate the limitations and prospects of AC. For non-ideal and semioptimal AC, we study the impact of finite relaxation times of reset and computation spins on the achievable effective cooling. We derive, via simulations, the attainable cooling levels for given ratios of relaxation times using two semioptimal practicable algorithms. We expect this analysis to be valuable for the planning of future experiments. For ideal and optimal AC, we make use of lower bounds on the number of required reset steps, based on entropy considerations, to present important consequences of using AC as a tool for improving signal-to-noise ratio in liquid-state magnetic resonance spectroscopy. We discuss the potential use of AC for noninvasive clinical diagnosis and drug monitoring, where it may have significantly lower specific absorption rate (SAR) with respect to currently used methods.

quant-ph↗
arXiv2013

Attacks on Fixed Apparatus Quantum Key Distribution Schemes

We consider quantum key distribution implementations in which the receiver's apparatus is fixed and does not depend on his choice of basis at each qubit transmission. We show that, although theoretical quantum key distribution is proven secure, such implementations are totally insecure against a strong eavesdropper that has one-time (single) access to the receiver's equipment. The attack we present here, the "fixed-apparatus attack" causes a potential risk to the usefulness of several recent implementations.

quant-ph↗
arXiv2013

Quantum Computing Gates via Optimal Control

We demonstrate the use of optimal control to design two entropy-manipulating quantum gates which are more complex than the corresponding, commonly used, gates, such as CNOT and Toffoli (CCNOT): A 2-qubit gate called PE (polarization exchange) and a 3-qubit gate called COMP (polarization compression) were designed using GRAPE, an optimal control algorithm. Both gates were designed for a three-spin system. Our design provided efficient and robust NMR radio frequency (RF) pulses for 13C2-trichloroethylene (TCE), our chosen three-spin system. We then experimentally applied these two quantum gates onto TCE at the NMR lab. Such design of these gates and others could be relevant for near-future applications of quantum computing devices.

quant-ph↗
arXiv2011

Heat-Bath Cooling of Spins in Two Amino Acids

Heat-bath cooling is a component of practicable algorithmic cooling of spins, an approach which might be useful for in vivo 13C spectroscopy, in particular for prolonged metabolic processes where substrates that are hyperpolarized ex-vivo are not effective. We applied heat-bath cooling to 1,2-13C2-amino acids, using the alpha protons to shift entropy from selected carbons to the environment. For glutamate and glycine, both carbons were cooled by about 2.5-fold, and in other experiments the polarization of C1 nearly doubled while all other spins had equilibrium polarization, indicating reduction in total entropy. The effect of adding Magnevist, a gadolinium contrast agent, on heat-bath cooling of glutamate was investigated.

quant-ph↗